A346681 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(5*k,k) / (4*k + 1).

1, 0, 5, 30, 255, 2275, 21476, 210404, 2120041, 21830314, 228713056, 2430255074, 26128088701, 283703487059, 3106713300821, 34270543858459, 380471319687826, 4247891403168599, 47665096853113576, 537244509843680309, 6079834137116933061, 69054467456964456599

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..925

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x)^4 * A(x)^5.

a(n) ~ 5^(5*n + 11/2) / (3381 * sqrt(Pi) * n^(3/2) * 2^(8*n + 7/2)). - Vaclav Kotesovec, Jul 30 2021

Mathematica

Table[Sum[(-1)^(n - k) Binomial[5 k, k]/(4 k + 1), {k, 0, n}], {n, 0, 21}]
nmax = 21; A[_] = 0; Do[A[x_] = 1/(1 + x) + x (1 + x)^4 A[x]^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(5*k, k)/(4*k + 1)); \\ Michel Marcus, Jul 29 2021

Crossrefs

Cf. A002294, A032357, A188678, A345368, A346665.

Cf. A346680, A346682, A346683, A346684.

Sequence in context: A072213 A257741 A308946 * A279155 A245247 A353547

Adjacent sequences: A346678 A346679 A346680 * A346682 A346683 A346684

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 29 2021

Status

approved