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A357245
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E.g.f. satisfies A(x) * log(A(x)) = 3 * (exp(x) - 1).
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1
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1, 3, -6, 84, -1599, 42906, -1477716, 62171661, -3090518556, 177237143040, -11518529575857, 836601742598628, -67156626492464064, 5904119985344031639, -564188922815428792914, 58225175660113940932032, -6453955474121138652732903, 764716767229825444834522086
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..17.
Eric Weisstein's World of Mathematics, Lambert W-Function.
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FORMULA
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a(n) = Sum_{k=0..n} 3^k * (-k+1)^(k-1) * Stirling2(n,k).
E.g.f.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * (3 * (exp(x) - 1))^k / k!.
E.g.f.: A(x) = exp( LambertW(3 * (exp(x) - 1)) ).
E.g.f.: A(x) = 3 * (exp(x) - 1)/LambertW(3 * (exp(x) - 1)).
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PROG
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(PARI) a(n) = sum(k=0, n, 3^k*(-k+1)^(k-1)*stirling(n, k, 2));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k+1)^(k-1)*(3*(exp(x)-1))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(3*(exp(x)-1)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(3*(exp(x)-1)/lambertw(3*(exp(x)-1))))
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CROSSREFS
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Cf. A349583, A357244.
Sequence in context: A213138 A349875 A331403 * A157197 A211896 A299433
Adjacent sequences: A357242 A357243 A357244 * A357246 A357247 A357248
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KEYWORD
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sign
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AUTHOR
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Seiichi Manyama, Sep 19 2022
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STATUS
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approved
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