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

0,3

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Row n=2 of A341847.

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

Sequence in context: A282619 A080252 A318694 * A277379 A227545 A127113

Adjacent sequences: A281430 A281431 A281432 * A281434 A281435 A281436

Keyword

nonn

Author

Andrew Howroyd, Oct 05 2017

Status

approved