A351263 Triangle read by rows: T(n,k) is the number of oriented graphs on n labeled nodes whose underlying graph is k-regular, k = 0..n-1.

1, 1, 2, 1, 0, 8, 1, 12, 48, 64, 1, 0, 384, 0, 1024, 1, 120, 4480, 35840, 61440, 32768, 1, 0, 59520, 0, 7618560, 0, 2097152, 1, 1680, 897792, 79278080, 1268449280, 3677356032, 1761607680, 268435456, 1, 0, 15368192, 0, 268535070720, 0, 4028679323648, 0, 68719476736

Offset: 1

Author

Andrew Howroyd, Feb 05 2022

Keywords

• nonn
• tabl

Comments

The sum of the in-degree and out-degree at each node is k.

Examples

			Triangle begins:
  1;
  1,   2;
  1,   0,     8;
  1,  12,    48,    64;
  1,   0,   384,     0,    1024;
  1, 120,  4480, 35840,   61440, 32768;
  1,   0, 59520,     0, 7618560,     0, 2097152;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..300 (rows 1..24)

Crossrefs

Row sums are A351264.

Main diagonal is A006125.

The unlabeled version is A350912.

Cf. A059441 (graphs).

Formula

T(n,k) = A059441(n,k)*2^(n*k/2). - Pontus von Brömssen, Apr 04 2022