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

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

Example

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

Prog

(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)!)))}

Crossrefs

Cf. A027907; A005119 (variant).

Sequence in context: A125222 A199670 A192783 * A187735 A200318 A120015

Adjacent sequences: A136165 A136166 A136167 * A136169 A136170 A136171

Keyword

nonn

Author

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

Status

approved