A136168 a(n) = (n-1)!*Sum_{i=1..n-1} (-1)^(i+1)*A027907(n-i+2,i+1)*a(n-i)/(n-i)! for n>0 with a(0)=1, where A027907 is the triangle of trinomial coefficients.

1, 3, 16, 120, 1140, 12972, 171216, 2571912, 43429680, 816108048, 16894168704, 381536713152, 9332214825024, 246215663789760, 6984603724315392, 211834855804295808, 6819603388970206464, 232454553855108173568

Offset: 0

Author

Paul D. Hanna, Dec 27 2007, Jan 24 2008

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 3x + 16x^2/2! + 120x^3/3! + 1140x^4/4! + 12972x^5/5! +...
		

Crossrefs

Cf. A027907; A005119 (variant).

Programs

PARI

{a(n)=if(n<0,0,if(n==0,1,(n-1)!*sum(i=1,n,(-1)^(i+1)*polcoeff((1+x+x^2)^(n-i+2),i+1)*a(n-i)/(n-i)!)))}

Formula

E.g.f. satisfies: A(x) = (1-x+x^2)^2/(1-2x)*A(x-x^2+x^3).