A286951 -id:A286951 - cp's OEIS frontend

A218462 Number of simple perfect matching graphs on 2n nodes.

1, 6, 101, 10413, 11557799

Offset: 1

Eric W. Weisstein, Mar 26 2013

Perfect matchings exist only for graphs with an even number of nodes.

Eric Weisstein's World of Mathematics, Perfect Matching

Cf. A218463 (connected simple perfect matching graphs).
Cf. A287652 (disconnected simple perfect matching graphs).
Cf. A286951.

a(n) = A218463(n) + A287652(n). - Eric W. Weisstein, May 29 2017

a(n) = A286951(2*n, n). - Andrew Howroyd, Sep 05 2019

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)).

Original entry on oeis.org

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

Andrew Howroyd, Sep 05 2019

			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;
  ...

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

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.

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

cp's OEIS Frontend

A218462 Number of simple perfect matching graphs on 2n nodes.

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