Sum pyramid of primes Given a number N, the challenge is to get the sum of the pyramid of N primes. To clarify things, here is an example:

Input: 4


We will list the first 4 primes, and then compute the sum of them. After that, we will compute the sums of the sums, and so on:

  2
    &gt; 5
  3     &gt; 13
    &gt; 8      &gt; 33
  5     &gt; 20
    &gt; 12
  7


You can see that the final result is 33. Here is another example, with N = 8:

   2
     &gt;   5
   3       &gt;  13
     &gt;   8       &gt;  33
   5       &gt;  20       &gt;  83
     &gt;  12       &gt;  50       &gt; 205
   7       &gt;  30       &gt; 122       &gt; 495
     &gt;  18       &gt;  72       &gt; 290       &gt; 1169
  11       &gt;  42       &gt; 168       &gt; 674
     &gt;  24       &gt;  96       &gt; 384
  13       &gt;  54       &gt; 216
     &gt;  30       &gt; 120
  17       &gt;  66
     &gt;  36
  19


You can see that the final result is 1169.

Here is another example with an odd N, N = 3:

 2
   &gt; 5
 3     &gt; 13
   &gt; 8
 5


This gives us 13 as the result

Your task is to write a program or a function, that takes an integer greater than 0, and output the final result.

Here are some test results:

1:  2
2:  5
3:  13
4:  33
5:  83
6:  205
7:  495
8:  1169
9:  2707
10: 6169
11: 13889
12: 30993
13: 68701
14: 151469
15: 332349
16: 725837
17: 1577751
18: 3413221
19: 7349029
20: 15751187
21: 33616925
22: 71475193
23: 151466705
24: 320072415
25: 674721797
26: 1419327223
27: 2979993519
28: 6245693407
29: 13068049163
30: 27297614797
31: 56929779663
32: 118543624847
33: 246475746269
34: 511766428817
35: 1061264813321
36: 2198298700845
37: 4548996804811
38: 9405003164065
39: 19429190057417
40: 40107799133677
41: 82736199371081
42: 170553108953473
43: 351333736092089
44: 723224546040181
45: 1487710742395387
46: 3058157261678325
47: 6282142186547177
48: 12896743408107403
49: 26460652594917673
50: 54262186256186881
51: 111224391050741687
52: 227896496141836195
53: 466805185374509003
54: 955904519939662217
55: 1956988697590280537
56: 4005572366722212927
57: 8196803221276230093
58: 16769645303734608963
59: 34300013739423719561
60: 70136585692535099353
61: 143371352962891226373
62: 292978031452308375001
63: 598482012866917021541
64: 1222083126601616763473
65: 2494459637841415902073
66: 5089478703050176444803
67: 10379794709536133386939
68: 21160351440305258275579
69: 43119914481530819445497
70: 87833066190052490228187
71: 178841897161848754603319
72: 364014682565128163812791
73: 740654046243174781813209
74: 1506496270380756958474835
75: 3063280375436290387756263
76: 6227039507615221644290617
77: 12655020557561801933128885
78: 25712267089927372837530869
79: 52230425385198423845305957
80: 106076955379202815098486497
81: 215397386589448754140867649
82: 437308717912632286770415395
83: 887706233370396897803709611
84: 1801721089699452657985592689
85: 3656329898231436156162865559
86: 7418972676822310377574227797
87: 15051599987013574096449515927
88: 30532404546282900804722616529
89: 61926565462373271494414919017
90: 125582269494835615524470915169
91: 254631689768733901573206365479
92: 516210444730946464864091626473
93: 1046330617753410129672316234861
94: 2120493010460433691014704829565
95: 4296639990460140795780826898943
96: 8704509990931940668688755806845
97: 17631229933967301681217551193565
98: 35706243541395815998303171050377
99: 72298621492552303967009812018997


This is code-golf, so the shortest amount of bytes wins!
J, 15 bytes

p:@i.+/ .*i.!&lt;:


Explanation:

Basically the same as my Mathematica answer.

p:@i.+/ .*i.!&lt;:
          i.!&lt;:    binomial coefficients
p:@i.              first n primes
     +/ .*         dot product