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A357244
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E.g.f. satisfies A(x) * log(A(x)) = 2 * (exp(x) - 1).
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1
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1, 2, -2, 22, -266, 4614, -102442, 2777030, -88914730, 3283693254, -137408080298, 6425417730758, -332055079469610, 18792899306652358, -1156017201432075946, 76796076655220486854, -5479395288838822143786, 417905042599836811225798, -33928512587303405767179178
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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..18.
Eric Weisstein's World of Mathematics, Lambert W-Function.
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FORMULA
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a(n) = Sum_{k=0..n} 2^k * (-k+1)^(k-1) * Stirling2(n,k).
E.g.f.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * (2 * (exp(x) - 1))^k / k!.
E.g.f.: A(x) = exp( LambertW(2 * (exp(x) - 1)) ).
E.g.f.: A(x) = 2 * (exp(x) - 1)/LambertW(2 * (exp(x) - 1)).
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PROG
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(PARI) a(n) = sum(k=0, n, 2^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)*(2*(exp(x)-1))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(2*(exp(x)-1)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(2*(exp(x)-1)/lambertw(2*(exp(x)-1))))
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CROSSREFS
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Cf. A349583, A357245.
Cf. A356908.
Sequence in context: A118326 A212847 A087405 * A001012 A040082 A014358
Adjacent sequences: A357241 A357242 A357243 * A357245 A357246 A357247
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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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