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Search: id:A135746
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| A135746 |
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E.g.f.: A(x) = Sum_{n>=0} exp(n*x)^n * x^n/n!. |
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+0
6
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| 1, 1, 3, 16, 137, 1536, 22417, 407884, 8920641, 230576320, 6928080641, 238375169484, 9288784476193, 406150114297552, 19761959813464065, 1062437048084297596, 62727815353861478273, 4045278841893314992896
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=0..n} C(n,k)*(k^2)^(n-k).
O.g.f.: Sum_{n>=0} x^n/(1 - n^2*x)^(n+1). [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 08 2009]
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(k^2)^(n-k))} (PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(k^2*x +x*O(x^n))*x^k/k!), n)}
(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-k^2*x +x*O(x^n))^(k+1)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 08 2009]
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CROSSREFS
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Cf. variants: A135742, A135743, A135744, A135745, A135747.
Sequence in context: A048802 A119392 A129043 this_sequence A006057 A002719 A020554
Adjacent sequences: A135743 A135744 A135745 this_sequence A135747 A135748 A135749
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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), Nov 27 2007
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