A113329 a(n) = Sum_{k=0..n} 4^k*A111146(n,k).

1, 4, 32, 272, 2400, 21792, 203008, 1940224, 19065344, 193410560, 2038078464, 22490167296, 262429339648, 3271314362368, 43955391856640, 640254018879488, 10121874150653952, 173145693892509696, 3186234896556752896

Offset: 0

Author

Philippe Deléham and Paul D. Hanna, Oct 26 2005

Keywords

• nonn

Examples

			A(x) = (1 + 4*x + 32*x^2 + 272*x^3 + 2400*x^4 + 21792*x^5 +..)
= 1/(1 - 4/3!*x*(3! + 4!*x + 5!*x^2 + 6!*x^3 + 7!*x^4 +..) ).
		

Crossrefs

Cf. A111146, A113326, A113327 (y=2), A113328 (y=3), A113330 (y=5), A113331 (y=6).

Programs

PARI

{a(n)=local(y=4,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 - (2/3)*x*Sum_{k>=0} (k+3)!*x^k ).