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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. 0
1, 3, 16, 120, 1140, 12972, 171216, 2571912, 43429680, 816108048, 16894168704, 381536713152, 9332214825024, 246215663789760, 6984603724315392, 211834855804295808, 6819603388970206464, 232454553855108173568 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 11 18:21 EDT 2021. Contains 343808 sequences. (Running on oeis4.)