A362857 Expansion of e.g.f. exp(-2*x) / (1 + LambertW(-x)).

1, -1, 4, 7, 120, 1373, 21028, 373931, 7670736, 178064281, 4615519884, 132139421423, 4141235867992, 141016013784917, 5184372688776180, 204668397165154867, 8635388122600110240, 387787185320578895537, 18467131524896950511644

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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

Formula

G.f.: Sum_{k>=0} (k*x)^k / (1 + 2*x)^(k+1).

a(n) = Sum_{k=0..n} (-2)^(n-k) * k^k * binomial(n,k).

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[-2x]/(1+LambertW[-x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 26 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2*x)/(1 + lambertw(-x))))

Crossrefs

Column k=2 of A362856.

Cf. A362859.

Sequence in context: A322723 A220003 A024054 * A289381 A126577 A236288

Adjacent sequences: A362854 A362855 A362856 * A362858 A362859 A362860

Keyword

sign

Author

Seiichi Manyama, May 05 2023

Status

approved