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A156326
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E.g.f.: A(x) = exp( Sum_{n>=1} n^2 * a(n-1)*x^n/n! ) = Sum_{n>=0} a(n)*x^n/n! with a(0)=1.
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3
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1, 1, 5, 58, 1181, 36696, 1601497, 92969920, 6908883417, 638746871680, 71860612355981, 9664570175364864, 1531263494465900725, 282321785979644121088, 59935663751282958139425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=1..n} k^2 * C(n-1,k-1)*a(k-1)*a(n-k) for n>0, with a(0)=1.
E.g.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where A(x/G(x)) = G(x) is the e.g.f. of A182962, which satisfies:
. G(x) = exp( x/(1 - x*G'(x)/G(x)) );
. a(n) = [x^n/n!] G(x)^(n+1)/(n+1) for n>=0.
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EXAMPLE
| E.g.f: A(x) = 1 + x + 5*x^2/2! + 58*x^3/3! + 1181*x^4/4! + 36696*x^5/5! +...
log(A(x)) = x + 2^2*x^2/2! + 3^2*5*x^3/3! + 4^2*58*x^4/4! + 5^2*1181*x^5/5! +...
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PROG
| (PARI) {a(n)=if(n==0, 1, n!*polcoeff(exp(sum(k=1, n, k^2*a(k-1)*x^k/k!)+x*O(x^n)), n))}
(PARI) {a(n)=if(n==0, 1, sum(k=1, n, k^2*binomial(n-1, k-1)*a(k-1)*a(n-k)))}
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CROSSREFS
| Cf. A156325, A156327, A182962.
Sequence in context: A097631 A130768 A195947 * A001624 A096476 A158694
Adjacent sequences: A156323 A156324 A156325 * A156327 A156328 A156329
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 08 2009
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