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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
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. A141209.
Sequence in context: A300127 A059735 A358213 * A134959 A270367 A056607
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.)