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A009199
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Expansion of e.g.f. exp(log(1+x)^2).
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7
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1, 0, 2, -6, 34, -220, 1688, -14868, 147684, -1631376, 19821912, -262573080, 3764276712, -58044604176, 957653604672, -16828739439120, 313742795670288, -6183918938706048, 128463999017594016, -2804979941504113248
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OFFSET
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0,3
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..446
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 128
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} Stirling1(n, 2*k)*(2*k)!/k!. - Vladeta Jovovic, Sep 21 2003
E.g.f.: (1+x)^(log(1+x)). - Vaclav Kotesovec, Jul 31 2018
a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n-1,k-1) * Stirling1(k,2) * a(n-k). - Seiichi Manyama, May 06 2022
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MATHEMATICA
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CoefficientList[Series[E^(Log[1+x]^2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 02 2015 *)
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PROG
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(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, binomial(i-1, j-1)*stirling(j, 2, 1)*v[i-j+1])); v; \\ Seiichi Manyama, May 06 2022
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CROSSREFS
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Sequence in context: A253778 A346189 A018953 * A052824 A019029 A019032
Adjacent sequences: A009196 A009197 A009198 * A009200 A009201 A009202
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KEYWORD
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sign,easy
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AUTHOR
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R. H. Hardin
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EXTENSIONS
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Extended with signs by Olivier Gérard, Mar 15 1997
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STATUS
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approved
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