A360787 Expansion of Sum_{k>=0} x^k / (1 - (k*x)^2)^(k+1).

1, 1, 1, 3, 13, 40, 177, 965, 4733, 28103, 184065, 1191888, 8713549, 67005689, 528870257, 4526024267, 40051790333, 368513578472, 3583302492545, 35868588067501, 373781214260749, 4052932682659599, 45218033687522481, 523234757502985824, 6245693941097387773

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

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

Mathematica

Join[{1}, Table[Sum[Binomial[n-k, k] * (n-2*k)^(2*k), {k, 0, n/2}], {n, 1, 30}]] (* Vaclav Kotesovec, Feb 21 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^2)^(k+1)))
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^(2*k)*binomial(n-k, k));

Crossrefs

Cf. A000248, A360788.

Cf. A360782, A360592.

Sequence in context: A059020 A290720 A289654 * A095109 A259764 A309139

Adjacent sequences: A360784 A360785 A360786 * A360788 A360789 A360790

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 20 2023

Status

approved