A346671 a(n) = Sum_{k=0..n} binomial(7*k,k) / (6*k + 1).

1, 2, 9, 79, 898, 11370, 153148, 2150836, 31140511, 461462144, 6964815000, 106691488130, 1654539334220, 25923944408960, 409770113121064, 6526344613981944, 104632592920840659, 1687270854882480906, 27348675382672733281, 445328790513987869681, 7281393330439106226281

Offset

0,2

Comments

Partial sums of A002296.

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) / (776887 * sqrt(Pi) * n^(3/2) * 2^(6*n + 2) * 3^(6*n + 3/2)). - Vaclav Kotesovec, Jul 30 2021

Mathematica

Table[Sum[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

(PARI) a(n) = sum(k=0, n, binomial(7*k, k)/(6*k+1)); \\ Michel Marcus, Jul 28 2021

Crossrefs

Cf. A002296, A014137, A104859, A345367, A345368, A346065, A346649, A346672.

Sequence in context: A111196 A229211 A056918 * A194471 A369712 A215629

Adjacent sequences: A346668 A346669 A346670 * A346672 A346673 A346674

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 28 2021

Status

approved