A325304 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with matching number k, (0 <= k <= floor(n/2)).

1, 1, 0, 1, 0, 2, 0, 1, 5, 0, 1, 20, 0, 1, 16, 95, 0, 1, 22, 830, 0, 1, 29, 790, 10297, 0, 1, 37, 1479, 259563, 0, 1, 46, 2625, 166988, 11546911

Offset: 0

Author

Andrew Howroyd, Sep 05 2019

Keywords

• nonn
• tabf
• more

Examples

			Triangle begins:
  1;
  1;
  0, 1;
  0, 2;
  0, 1,  5;
  0, 1, 20;
  0, 1, 16,   95;
  0, 1, 22,  830;
  0, 1, 29,  790,  10297;
  0, 1, 37, 1479, 259563;
  0, 1, 46, 2625, 166988, 11546911;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Matching Number
• Wikipedia, Matching (graph theory)

Crossrefs

Columns k=2..3 are A243800, A243801.

Row sums are A001349.

Cf. A286951 (not necessarily connected).

Cf. A218463 (right diagonal, even terms).

Cf. A263341, A294490.

Formula

T(2*n, n) = A218463(n).