A362395 E.g.f. satisfies A(x) = exp(x - x^2/2 * A(x)).

1, 1, 0, -5, -14, 56, 736, 1114, -45156, -428660, 2004796, 82797716, 446153632, -13593781928, -276074700264, 701782138576, 107474258830096, 1263010302870608, -30208216250914352, -1146149464640506928, -2087509382334856224, 703335832718961413056

Offset: 0

Author

Seiichi Manyama, Apr 20 2023

Keywords

• sign

Links

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

Crossrefs

Column k=1 of A362394.

Cf. A143740.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2/2*exp(x)))))

Formula

E.g.f.: exp(x - LambertW(x^2/2 * exp(x))) = 2 * LambertW(x^2/2 * exp(x))/x^2.

a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).