A113146 Row 5 of table A113143; equal to INVERT of quintic (or 5-fold) factorials shifted one place right.

1, 1, 2, 9, 83, 1226, 24727, 627909, 19169758, 682800001, 27776711627, 1270110048234, 64470498348983, 3596569233141701, 218698213338646702, 14395754017090902609, 1019782749198898131883, 77351848007810972904826

Offset: 0

Author

Philippe Deléham and Paul D. Hanna, Oct 28 2005

Keywords

• nonn

Examples

			A(x) = 1 + x + 2*x^2 + 9*x^3 + 83*x^4 + 1226*x^5 +...
= 1/(1 - x - x^2 - 6*x^3 - 66*x^4 -...- A008548(n)*x^(n+1)
-...).
		

Crossrefs

Cf. A113143, A008548 (5-fold factorials).

Programs

PARI

{a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0,n,x^j*prod(i=0,j,5*i+1)));return(polcoeff(A,n,X))}

Formula

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

a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A008548(n-k).