A346682 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(6*k,k) / (5*k + 1).

1, 0, 6, 45, 461, 5020, 57812, 691586, 8512048, 107095262, 1371219004, 17808830924, 234048288772, 3106795261083, 41593689788637, 560980967638479, 7614970691479315, 103957059568762775, 1426355910771621805, 19658792867492660060, 272046427837226505466

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..856

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x)^5 * A(x)^6.

a(n) ~ 2^(6*n + 6) * 3^(6*n + 13/2) / (49781 * sqrt(Pi) * n^(3/2) * 5^(5*n + 3/2)). - Vaclav Kotesovec, Jul 30 2021

Mathematica

Table[Sum[(-1)^(n - k) Binomial[6 k, k]/(5 k + 1), {k, 0, n}], {n, 0, 20}]
nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 + x) + x (1 + x)^5 A[x]^6 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*k, k)/(5*k + 1)); \\ Michel Marcus, Jul 29 2021

Crossrefs

Cf. A002295, A032357, A188678, A346065, A346666.

Cf. A346680, A346681, A346683, A346684.

Sequence in context: A186925 A368793 A294642 * A109516 A245493 A078865

Adjacent sequences: A346679 A346680 A346681 * A346683 A346684 A346685

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 29 2021

Status

approved