A333158 Irregular triangle read by rows: T(n,k) is the number of k-regular graphs on n labeled nodes with loops allowed, n >= 1, 0 <= k <= n + 1.

1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 1, 3, 8, 8, 3, 1, 1, 0, 38, 0, 38, 0, 1, 1, 15, 208, 730, 730, 208, 15, 1, 1, 0, 1348, 0, 20670, 0, 1348, 0, 1, 1, 105, 10126, 188790, 781578, 781578, 188790, 10126, 105, 1, 1, 0, 86174, 0, 37885204, 0, 37885204, 0, 86174, 0, 1

Offset: 1

Author

Andrew Howroyd, Mar 09 2020

Keywords

• nonn
• tabf

Comments

A loop adds 2 to the degree of its vertex.

Examples

			Triangle begins:
  1,   0,     1;
  1,   1,     1,      1;
  1,   0,     2,      0,      1;
  1,   3,     8,      8,      3,      1;
  1,   0,    38,      0,     38,      0,      1;
  1,  15,   208,    730,    730,    208,     15,     1;
  1,   0,  1348,      0,  20670,      0,   1348,     0,   1;
  1, 105, 10126, 188790, 781578, 781578, 188790, 10126, 105, 1;
  ...
		

Crossrefs

Row sums are A322635.

Columns k=0..4 are A000012, A123023, A108246, A110039 (with interspersed zeros), A228697.

Cf. A059441, A333157.

Formula

T(n,k) = T(n, n+1-k).