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A136168
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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.
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0
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1, 3, 16, 120, 1140, 12972, 171216, 2571912, 43429680, 816108048, 16894168704, 381536713152, 9332214825024, 246215663789760, 6984603724315392, 211834855804295808, 6819603388970206464, 232454553855108173568
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| E.g.f. satisfies: A(x) = (1-x+x^2)^2/(1-2x)*A(x-x^2+x^3).
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EXAMPLE
| E.g.f.: A(x) = 1 + 3x + 16x^2/2! + 120x^3/3! + 1140x^4/4! + 12972x^5/5! +...
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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)!)))}
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CROSSREFS
| Cf. A027907; A005119 (variant).
Sequence in context: A125222 A199670 A192783 * A200318 A120015 A003692
Adjacent sequences: A136165 A136166 A136167 * A136169 A136170 A136171
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 27 2007, Jan 24 2008
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