<p>Illustration of the triangle <span style="white-space:nowrap"><a href="https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="Sloane's"><img alt="Sloane's" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556"></a> <a href="//oeis.org/A008284" class="extiw" title="oeis:A008284">A008284</a></span><br>
showing the number of <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)" class="extiw" title="w:Partition (number theory)">partitions</a> of <i>n</i> <small>(top to bottom, starting from 1)</small> with <i>k</i> <small>(left to right, starting from 1)</small> addends<br>
The partitions are represented by <a href="https://en.wikipedia.org/wiki/Young_tableau" class="extiw" title="w:Young tableau">Young diagrams</a>.<br>
The row sums on the right are the partition numbers <span style="white-space:nowrap"><a href="https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="Sloane's"><img alt="Sloane's" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556"></a> <a href="//oeis.org/A000041" class="extiw" title="oeis:A000041">A000041</a></span>.
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The big numbers (in Times New Roman) show the number of partitions in the respective box of the triangle.<br>
The small numbers (in Arial) show the index number of the partition below (compare <a href="//commons.wikimedia.org/wiki/File:Partitions_of_10.svg#File" title="File:Partitions of 10.svg"><b>this</b></a> table).
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Compare:<br></p>
<div class="thumb tleft"><div class="thumbinner" style="width:302px;"><a href="//commons.wikimedia.org/wiki/File:Partitions_of_n_with_biggest_addend_k.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Partitions_of_n_with_biggest_addend_k.svg/300px-Partitions_of_n_with_biggest_addend_k.svg.png" decoding="async" width="300" height="246" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Partitions_of_n_with_biggest_addend_k.svg/450px-Partitions_of_n_with_biggest_addend_k.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Partitions_of_n_with_biggest_addend_k.svg/600px-Partitions_of_n_with_biggest_addend_k.svg.png 2x" data-file-width="1350" data-file-height="1108"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Partitions_of_n_with_biggest_addend_k.svg" class="internal" title="Enlarge"></a></div>With biggest addend <i>k</i><br>(reflected Young diagrams)</div></div></div><div class="thumb tright"><div class="thumbinner" style="width:302px;"><a href="//commons.wikimedia.org/wiki/File:Partition_necklaces.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Partition_necklaces.svg/300px-Partition_necklaces.svg.png" decoding="async" width="300" height="300" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Partition_necklaces.svg/450px-Partition_necklaces.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Partition_necklaces.svg/600px-Partition_necklaces.svg.png 2x" data-file-width="1350" data-file-height="1350"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Partition_necklaces.svg" class="internal" title="Enlarge"></a></div>Set partitions up to rotation and reflection</div></div></div>
<table><tbody><tr><td style="padding: 15px;"><a href="//commons.wikimedia.org/wiki/File:Watchduck.svg" class="image"><img alt="Watchduck.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/40px-Watchduck.svg.png" decoding="async" width="40" height="46" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/60px-Watchduck.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Watchduck.svg/80px-Watchduck.svg.png 2x" data-file-width="703" data-file-height="806"></a>
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<td><a href="//commons.wikimedia.org/wiki/User:Watchduck" title="User:Watchduck">Watchduck</a><br><span style="color: gray; font-size: 80%;">You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".</span>
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<span class="int-own-work" lang="en">Own work</span>