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

0,4

Comments

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

Links

Table of n, a(n) for n=0..65.

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

Example

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
  ...

Crossrefs

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

Sequence in context: A193795 A181355 A128320 * A348436 A350528 A208057

Adjacent sequences: A189504 A189505 A189506 * A189508 A189509 A189510

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 23 2011

Status

approved