A360483 E.g.f. satisfies A(x) = x * exp(x - 2 * A(x)).

0, 1, -2, 15, -172, 2685, -53226, 1281091, -36296408, 1183527225, -43660076950, 1797823266591, -81746462498724, 4068086310006901, -219929012455113794, 12835335232410655035, -804287930238495495856, 53858337558670992931185

Offset: 0

Author

Seiichi Manyama, Feb 09 2023

Keywords

• sign

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A216857, A360481, A360482, A360484.

Programs

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));

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).