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A281433
Number of maximal matchings in the 2 X n rook graph.
3
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 05 2017
STATUS
approved