A008326 Triangle read by rows: T(n,k) is the number of simple regular connected bipartite graphs with 2n nodes and degree k, (2 <= k <= n).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 4, 1, 1, 1, 13, 14, 4, 1, 1, 1, 38, 129, 41, 7, 1, 1, 1, 149, 1980, 1981, 157, 8, 1, 1, 1, 703, 62611, 304495, 62616, 725, 12, 1, 1, 1, 4132, 2806490, 78322915, 78322916, 2806508, 4196, 14, 1, 1, 1, 29579, 158937213, 27033154060, 147252447227, 27033154065, 158937367, 29817, 21, 1, 1

Offset

2,8

Comments

This sequence can be derived from A133687 and A333159. In particular, if w(n) is the inverse Euler transform of column k of A133687 and s(n) is the inverse Euler transform of column k of A333159, then 2*T(2*n+1,k) = w(2*n+1) + s(2*n+1) and 2*T(2*n,k) = w(2*n) + s(2*n) - w(n) + T(n,k). - Andrew Howroyd, Apr 03 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 2..154

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

Example

Triangle begins:
  1;
  1,   1;
  1,   1,    1;
  1,   2,    1,    1;
  1,   5,    4,    1,   1;
  1,  13,   14,    4,   1, 1;
  1,  38,  129,   41,   7, 1, 1;
  1, 149, 1980, 1981, 157, 8, 1, 1;
  ...

Crossrefs

Columns k=3..7 are A006823, A006824, A006825, A014385, A014387.

Row sums are in A008323.

Cf. A008327, A133687, A333159.

Sequence in context: A347615 A241194 A352893 * A181196 A227578 A181783

Adjacent sequences: A008323 A008324 A008325 * A008327 A008328 A008329

Keyword

nonn,hard,tabl

Author

Brendan McKay and Eric Rogoyski

Extensions

More terms from Eric Rogoyski, May 15 1997

Name clarified by Andrew Howroyd, Sep 05 2018

Terms a(55) and beyond from Andrew Howroyd, Apr 03 2020

Status

approved