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 A356926 E.g.f. satisfies A(x)^A(x) = 1/(1 - x)^exp(x). 1
 1, 1, 2, 3, 10, 35, 121, 1092, 5216, 39321, 558643, 2433508, 48144944, 688652549, 2176310995, 145742587616, 1334993574032, 5551320939809, 799648465754835, 1049695714507276, 90069170433616208, 6281942689646504501, -53282051261767839293, 2356158301117802408472 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..23. Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA E.g.f.: A(x) = Sum_{k>=0} (-k+1)^(k-1) * (-exp(x) * log(1-x))^k / k!. E.g.f.: A(x) = exp( LambertW(-exp(x) * log(1-x)) ). E.g.f.: A(x) = -exp(x) * log(1-x)/LambertW(-exp(x) * log(1-x)). MATHEMATICA nmax = 23; A[_] = 1; Do[A[x_] = ((1 - x)^(-Exp[x]))^(1/A[x]) + O[x]^(nmax+1) // Normal, {nmax}]; CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *) PROG (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k+1)^(k-1)*(-exp(x)*log(1-x))^k/k!))) (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(-exp(x)*log(1-x))))) (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*log(1-x)/lambertw(-exp(x)*log(1-x)))) CROSSREFS Cf. A191365, A356925. Cf. A356912, A356913. Cf. A002104, A177885. Cf. A141209. Sequence in context: A300127 A059735 A358213 * A134959 A270367 A056607 Adjacent sequences: A356923 A356924 A356925 * A356927 A356928 A356929 KEYWORD sign AUTHOR Seiichi Manyama, Sep 04 2022 STATUS approved

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Last modified April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)