A360782 Expansion of Sum_{k>=0} x^k / (1 - k*x^2)^(k+1).

1, 1, 1, 3, 7, 16, 45, 125, 363, 1127, 3561, 11696, 39727, 138113, 494213, 1811075, 6784115, 25985928, 101520833, 404305549, 1640002039, 6767576175, 28395916893, 121048681024, 523902418555, 2300906314849, 10248029334297, 46266088140291

Offset

0,4

Links

Table of n, a(n) for n=0..27.

Formula

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

Mathematica

Join[{1}, Table[Sum[Binomial[n-k, k] * (n-2*k)^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)^k*binomial(n-k, k));

Crossrefs

Cf. A000248, A360783.

Cf. A000045, A360592.

Sequence in context: A129045 A217358 A323692 * A351821 A005312 A341576

Adjacent sequences: A360779 A360780 A360781 * A360783 A360784 A360785

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 20 2023

Status

approved