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 A357243 E.g.f. satisfies A(x)^A(x) = 1/(1 - x)^(1 - x). 2
 1, 1, -2, 6, -52, 540, -7608, 129304, -2612608, 60867360, -1608663840, 47527158624, -1552431588288, 55547889458880, -2160724031160576, 90782738645280000, -4097139872604807168, 197675862365363088384, -10153243488783257091072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA E.g.f. satisfies A(x)^A(x) * (1 - x)^(1 - x) = 1. E.g.f.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * (-(1-x) * log(1-x))^k / k!. E.g.f.: A(x) = exp( LambertW(-(1-x) * log(1-x)) ). E.g.f.: A(x) = -(1-x) * log(1-x)/LambertW(-(1-x) * log(1-x)). PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k+1)^(k-1)*(-(1-x)*log(1-x))^k/k!))) (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(-(1-x)*log(1-x))))) (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1-x)*log(1-x)/lambertw(-(1-x)*log(1-x)))) CROSSREFS Cf. A005727, A155456, A349561, A356905, A356908. Sequence in context: A027263 A320453 A277477 * A277363 A156340 A337510 Adjacent sequences: A357240 A357241 A357242 * A357244 A357245 A357246 KEYWORD sign AUTHOR Seiichi Manyama, Sep 19 2022 STATUS approved

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Last modified February 4 04:43 EST 2023. Contains 360046 sequences. (Running on oeis4.)