OFFSET
0,2
COMMENTS
Partial sums of A002294.
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) / (2869 * sqrt(Pi) * n^(3/2) * 2^(8*n + 7/2)). - Vaclav Kotesovec, Jul 28 2021
MATHEMATICA
Table[Sum[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, binomial(5*k, k)/(4*k+1)); \\ Michel Marcus, Jul 28 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 28 2021
STATUS
approved