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A337465
a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).
1
1, 5, -6, -139, 1654, -5853, -196860, 6258751, -112580442, 985287863, 26443436876, -1897380617625, 72596047613116, -2086036395460171, 39493340495025864, 304974352009838745, -85532651616832374010, 6040114369000387188975, -321378391411642082323524, 14224299551865677212271567
OFFSET
0,2
MATHEMATICA
a[n_] := Sum[If[n == n - k == 0, 1, (-n)^(n-k)] * Binomial[2*k, k] * Binomial[2*n+1, 2*k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Apr 29 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n, (-n)^(n-k)*binomial(2*k, k)*binomial(2*n+1, 2*k))}
CROSSREFS
Main diagonal of A337464.
Sequence in context: A078984 A266718 A041257 * A041411 A103089 A041601
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 28 2020
STATUS
approved