A008327 Triangle read by rows: T(n,k) is the number of simple regular bipartite graphs with 2n nodes and degree k, (0 <= k <= n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 4, 6, 4, 1, 1, 1, 1, 4, 14, 14, 4, 1, 1, 1, 1, 7, 41, 130, 41, 7, 1, 1, 1, 1, 8, 157, 1981, 1981, 157, 8, 1, 1, 1, 1, 12, 725, 62616, 304496, 62616, 725, 12, 1, 1, 1, 1, 14, 4196, 2806508, 78322916

Offset

0,13

Comments

This sequence can be derived from A008326 by Euler transform. - Andrew Howroyd, Apr 03 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 0..189

B. D. McKay and E. Rogoyski, Latin squares of order ten, Electron. J. Combinatorics, 2 (1995) #N3.

Formula

Column k is the Euler transform of column k of A008326. - Andrew Howroyd, Apr 03 2020

Example

Triangle begins:
  1,
  1, 1,
  1, 1, 1,
  1, 1, 1,   1,
  1, 1, 2,   1,    1,
  1, 1, 2,   2,    1,    1,
  1, 1, 4,   6,    4,    1,   1;
  1, 1, 4,  14,   14,    4,   1, 1;
  1, 1, 7,  41,  130,   41,   7, 1, 1;
  1, 1, 8, 157, 1981, 1981, 157, 8, 1, 1;
  ...

Crossrefs

Column k=0..5 are A000012, A000012, A002865, A008325, A333730, A333731.

Row sums are A008324.

Cf. A051031, A008326, A087114, A133687, A333159.

Sequence in context: A227690 A063686 A333159 * A133687 A215870 A097587

Adjacent sequences: A008324 A008325 A008326 * A008328 A008329 A008330

Keyword

nonn,tabl,nice

Author

Brendan McKay

Extensions

More terms from Eric Rogoyski, May 15 1997

Name clarified by Andrew Howroyd, Sep 05 2018

Status

approved