A363305 Expansion of g.f. A(x) satisfying A(x) = 1 + x*(A(x)^5 + A(x)^9).

1, 2, 28, 576, 13968, 371280, 10465152, 307252032, 9295409664, 287758274304, 9071667965184, 290237226038272, 9399819302979584, 307570021821937664, 10152439243763290112, 337658352835320934400, 11304320019217804476416, 380650592731460987617280

Offset: 0

Author

Paul D. Hanna, May 29 2023

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 28*x^2 + 576*x^3 + 13968*x^4 + 371280*x^5 + 10465152*x^6 + 307252032*x^7 + 9295409664*x^8 + ...
where A(x) = 1 + x*(A(x)^5 + A(x)^9).
RELATED SERIES.
A(x)^5 = 1 + 10*x + 180*x^2 + 4080*x^3 + 104160*x^4 + 2858352*x^5 + 82336320*x^6 + 2455727040*x^7 + ...
A(x)^9 = 1 + 18*x + 396*x^2 + 9888*x^3 + 267120*x^4 + 7606800*x^5 + 224915712*x^6 + 6839682624*x^7 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A027307, A363311, A363304.

Programs

PARI

{a(n) = sum(k=0, n, binomial(n, k)*binomial(5*n+4*k+1, n)/(5*n+4*k+1) )}
for(n=0, 20, print1(a(n), ", "))

Formula

G.f.: A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.

(1) A(x) = 1 + x*(A(x)^5 + A(x)^9).

(2) a(n) = Sum_{k=0..n} binomial(n, k)*binomial(5*n+4*k+1, n)/(5*n+4*k+1) for n >= 0.