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A357335
E.g.f. satisfies A(x) = (exp(x) - 1) * exp(2 * A(x)).
3
0, 1, 5, 49, 757, 16081, 435477, 14345297, 556857973, 24894290257, 1259621627349, 71165987957329, 4440821632449077, 303338709537825105, 22512353926895739797, 1803812930088064925265, 155195078834104237961717, 14270228623788585753803089
OFFSET
0,3
FORMULA
E.g.f.: -LambertW(2 * (1 - exp(x)))/2.
a(n) = Sum_{k=1..n} (2 * k)^(k-1) * Stirling2(n,k).
a(n) ~ sqrt(1 + 2*exp(1)) * n^(n-1) / (2 * exp(n) * log(1 + exp(-1)/2)^(n - 1/2)). - Vaclav Kotesovec, Nov 14 2022
E.g.f.: Series_Reversion( log(1 + x * exp(-2*x)) ). - Seiichi Manyama, Sep 09 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(2*(1-exp(x)))/2)))
(PARI) a(n) = sum(k=1, n, (2*k)^(k-1)*stirling(n, k, 2));
CROSSREFS
Cf. A357347.
Sequence in context: A145088 A301386 A192557 * A290755 A062995 A293847
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 24 2022
STATUS
approved