How should I recover my NTFS partition that I have accidentally deleted on my Mac
The NTFS volume has been recovered in a TeamViewer session. The method is slightly related to my answer here: Can't see external HDD partition in Disk Utility

Preface:

The NTFS volume was formatted attached to a Mexican-Spanish (or French?) Windows system.

The specific string "BOOTMGR" to find the NTFS Partition Boot Sector with grep wasn't successful because on these systems - as it later transpired - the proper string is "bootmgr" instead.

Assumptions:

The vanished partition and its important blocks weren't overwritten. The partition is situated near the "end" of the disk.



So the following method was used:


Enable and log-in as root and install wxHexEditor
get the device identifier with diskutil list. Below I assume it's disk2.
Open the device disk2 in wxHexEditor, jump to the very end of the disk and backward-search for the string "NTFS" which revealed the (2nd) Partition Boot Sector of the NTFS volume.
With its byte offset the block number of the last NTFS volume block can be determined (byte offset/512 + 1 = block number)
The (2nd) Partition Boot Sector contains the size of the whole NTFS volume in sectors at offset 0x028 and a field length of 8 Bytes and the sector size at offset 0x0B and a field length of 2 Bytes.


Sector size: 00 02 (= 512 Byte)
volume size in sectors was (after a 64bit to decimal conversion) 2047997951+1 blocks (one has to add 1 to the number of blocks because block count starts at 0!)

In Terminal the partition was added with fdisk:

fdisk -e /dev/disk2
edit 2 #add second partition
Partition id ('0' to disable)  [0 - FF]: [0] (? for help) 7 #HPFS/QNX/AUX
Do you wish to edit in CHS mode? [n] n
Partition offset [0 - 3907029167]: [446333006] 1859028992
Partition size [1 - 2048000175]: [2048000175] 2047997952
write
exit

the volume was mounted automatically.
The NTFS volume was checked with Paragon NTFS for Mac with a "no errors" result.




The initial details of at least one of the two deleted partitions posted by the OP were wrong:


First partition: 280 GB
Second partition: 1720 GB


The second partition had and has a size of 1.049 TB only!