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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 28 2021
STATUS
approved