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

Author

Brendan McKay and Eric Rogoyski

Keywords

• nonn
• hard
• tabl

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

Examples

			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;
  ...
		

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.

Crossrefs

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

Row sums are in A008323.

Cf. A008327, A133687, A333159.

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