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Search: id:A143740
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| A143740 |
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E.g.f.: A(x) = exp(x + x^2*A(x)/2). |
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+0
1
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| 1, 1, 2, 7, 34, 216, 1696, 15898, 173468, 2161036, 30282076, 471599316, 8082816160, 151218316120, 3066890630168, 67031194526416, 1570793031033616, 39290173530686544, 1044871388684004304, 29440090627527552976
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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E.g.f.: A(x) = -2*LambertW( -x^2*exp(x)/2 )/x^2.
E.g.f.: A(x) = Sum_{n>=0} (n+1)^(n-1)*(x^2/2)^n*exp((n+1)*x)/n!.
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 34*x^4/4! + 216*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=exp(x+x^2*A/2)); (n+0)!*polcoeff(A, n)}
(PARI) {a(n)=local(A=sum(m=0, n, (m+1)^(m-1)*(x^2/2)^m*exp((m+1)*x+x*O(x^n))/m!)); n!*polcoeff(A, n)}
(PARI) {a(n)=local(Ex=exp(x+x*O(x^n)), W=Ex); for(k=0, n, W=exp(x*W)); n!*polcoeff(subst(W, x, x^2*Ex/2)*Ex, n)}
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CROSSREFS
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Cf. A125500.
Sequence in context: A111539 A074059 A135882 this_sequence A049463 A029894 A110313
Adjacent sequences: A143737 A143738 A143739 this_sequence A143741 A143742 A143743
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 30 2008
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