A113330 a(n) = Sum_{k=0..n} 5^k*A111146(n,k).

1, 5, 50, 525, 5675, 62650, 703975, 8042625, 93454750, 1106250125, 13377432875, 165950540250, 2124087269375, 28260204825625, 394301229688750, 5824314672613125, 91872380184761875, 1557002324898406250

Offset: 0

Author

Philippe Deléham and Paul D. Hanna, Oct 26 2005

Keywords

• nonn

Examples

			A(x) = (1 + 5*x + 50*x^2 + 525*x^3 + 5675*x^4 + 62650*x^5 +..)
= 1/(1 - 5/4!*x*(4! + 5!*x + 6!*x^2 + 7!*x^3 + 8!*x^4 +..) ).
		

Crossrefs

Cf. A111146, A113326, A113327 (y=2), A113328 (y=3), A113329 (y=4), A113331 (y=6).

Programs

PARI

{a(n)=local(y=5,x=X+X*O(X^n)); polcoeff(1/(1 - y/(y-1)!*x*sum(k=0,n,(y-1+k)!*x^k)),n,X)}

Formula

G.f.: A(x) = 1/(1 - (5/24)*x*Sum_{k>=0} (k+4)!*x^k ).