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A360484
E.g.f. satisfies A(x) = x * exp(x - 3 * A(x)).
3
0, 1, -4, 48, -896, 22880, -743232, 29337280, -1363752448, 72979407360, -4419108684800, 298730433250304, -22300928914403328, 1822195561572585472, -161756111552270491648, 15501595224386724126720, -1595092357302221461127168, 175405731698165304882495488
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: A(x) = LambertW(3*x * exp(x))/3.
a(n) = Sum_{k=1..n} (-3)^(k-1) * k^(n-1) * binomial(n,k).
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(3*x*exp(x))/3)))
(PARI) a(n) = sum(k=1, n, (-3)^(k-1)*k^(n-1)*binomial(n, k));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 09 2023
STATUS
approved