A346683 - OEIS

A346683

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(7*k,k) / (6*k + 1).

1, 0, 7, 63, 756, 9716, 132062, 1865626, 27124049, 403197584, 6100155272, 93626517858, 1454221328232, 22815183746508, 361030984965596, 5755543515895284, 92350704790963431, 1490287557170676816, 24171116970619575559, 393808998160695560841, 6442255541764422795759

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OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..806

FORMULA

G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x)^6 * A(x)^7.

a(n) ~ 7^(7*n + 15/2) / (870199 * sqrt(Pi) * n^(3/2) * 2^(6*n + 2) * 3^(6*n + 3/2)). - Vaclav Kotesovec, Jul 30 2021

MATHEMATICA

Table[Sum[(-1)^(n - k) Binomial[7 k, k]/(6 k + 1), {k, 0, n}], {n, 0, 20}]

nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 + x) + x (1 + x)^6 A[x]^7 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

PROG