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A360483
E.g.f. satisfies A(x) = x * exp(x - 2 * A(x)).
3
0, 1, -2, 15, -172, 2685, -53226, 1281091, -36296408, 1183527225, -43660076950, 1797823266591, -81746462498724, 4068086310006901, -219929012455113794, 12835335232410655035, -804287930238495495856, 53858337558670992931185
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: A(x) = LambertW(2*x * exp(x))/2.
a(n) = Sum_{k=1..n} (-2)^(k-1) * k^(n-1) * binomial(n,k).
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(2*x*exp(x))/2)))
(PARI) a(n) = sum(k=1, n, (-2)^(k-1)*k^(n-1)*binomial(n, k));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 09 2023
STATUS
approved