A281433 Number of maximal matchings in the 2 X n rook graph.

1, 1, 2, 10, 40, 296, 1576, 15352, 104000, 1276480, 10556416, 156843776, 1533722752, 26777626240, 302395339520, 6068829396736, 77740741758976, 1763457842941952, 25267740818452480, 639308368122204160, 10131932297407840256, 282891828731667890176

Offset: 0

Author

Andrew Howroyd, Oct 05 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100 (corrected by Ray Chandler, Jan 19 2019)

Crossrefs

Row n=2 of A341847.

Cf. A081919 (perfect matchings), A270229, A289198.

Programs

Mathematica

a[n_] := Sum[(2*k-1)!!^2 * Binomial[n, 2*k] * (1 + 2*k*(n-2*k)), {k, 0, n/2} ]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

PARI

a(n) = sum(k=0, n\2, ((2*k)!/(2^k*k!))^2 * binomial(n,2*k) * (1 + 2*k*(n-2*k)));

Formula

a(n) = Sum_{k=0..n/2} (2*k-1)!!^2 * binomial(n,2*k) * (1 + 2*k*(n-2*k)).