A113328 a(n) = Sum_{k=0..n} 3^k*A111146(n,k).

1, 3, 18, 117, 801, 5724, 42633, 331911, 2717874, 23620329, 220260789, 2228505372, 24681015981, 300506801715, 4017984855786, 58675338993069, 928673101727001, 15804592586240220, 287174716511520033, 5538727108037507535

Offset: 0

Author

Philippe Deléham and Paul D. Hanna, Oct 26 2005

Keywords

• nonn

Examples

			A(x) = (1 + 3*x + 18*x^2 + 117*x^3 + 801*x^4 + 5724*x^5 +..)
= 1/(1 - 3/2!*x*(2! + 3!*x + 4!*x^2 + 5!*x^3 + 6!*x^4 +..) ).
		

Crossrefs

Cf. A111146, A113326, A113327 (y=2), A113329 (y=4), A113330 (y=5), A113331 (y=6).

Programs

PARI

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