A189507 Triangle read by rows: T(n,k) (n >= 0, 1 <= k <= n+1) are the signed Hultman numbers.

1, 1, 1, 4, 3, 1, 20, 21, 6, 1, 148, 160, 65, 10, 1, 1348, 1620, 701, 155, 15, 1, 15104, 19068, 9324, 2247, 315, 21, 1, 198144, 264420, 138016, 38029, 5908, 574, 28, 1, 2998656, 4166880, 2325740, 692088, 124029, 13524, 966, 36, 1, 51290496, 74011488, 43448940, 13945700, 2723469, 344961, 27930, 1530, 45, 1, 979732224, 1459381440, 897020784, 305142068, 64711856, 8996295, 850905, 53262, 2310, 55, 1

Offset: 0

Author

N. J. A. Sloane, Apr 23 2011

Keywords

• nonn
• tabl

Comments

"Signed" refers to the fact that these numbers are associated with signed permutations. The numbers themselves are positive.

Examples

			Triangle begins:
      1
      1     1
      4     3    1
     20    21    6    1
    148   160   65   10   1
   1348  1620  701  155  15  1
  15104 19068 9324 2247 315 21 1
  ...
		

Links

• N. Alexeev, A. Pologova, M. A. Alekseyev, Generalized Hultman Numbers and Cycle Structures of Breakpoint Graphs, Journal of Computational Biology 24:2 (2017), 93-105. doi:10.1089/cmb.2016.0190 arXiv:1503.05285
• Simona Grusea and Anthony Labarre, The distribution of cycles in breakpoint graphs of signed permutations, arXiv:1104.3353v1

Crossrefs

The first three columns give A001171, A189508, A189509. Cf. A164652.