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A376107
Expansion of e.g.f. LambertW(x / (1 - 3*x)).
1
0, 1, 4, 27, 260, 3265, 50634, 935263, 20053816, 489677697, 13416375950, 407609962111, 13600700469828, 494442286466401, 19452778285314178, 823489845351967935, 37323572563440199664, 1803303384581598518785, 92523649833821902792086
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f. A(x) satisfies A(x) = x * (3*A(x) + exp(-A(x))).
E.g.f.: Series_Reversion( x / (3*x + exp(-x)) ).
a(n) = n! * Sum_{k=1..n} 3^(n-k) * (-k)^(k-1) * binomial(n-1,k-1)/k!.
MATHEMATICA
nmax=20; CoefficientList[InverseSeries[Series[x / (3*x + E^(-x)), {x, 0, nmax}], x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Sep 20 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(x/(1-3*x)))))
(PARI) a(n) = n!*sum(k=1, n, 3^(n-k)*(-k)^(k-1)*binomial(n-1, k-1)/k!);
CROSSREFS
Cf. A376101.
Sequence in context: A302836 A301335 A362701 * A177379 A052813 A218653
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2024
STATUS
approved