A321968 a(n) = 2^n*n!*[x^n] -sqrt(exp(LambertW(-x)))*(LambertW(-x) + 1).

-1, 3, 7, 55, 735, 13851, 336743, 10024911, 353109375, 14361853555, 662358958599, 34154042002983, 1947046027041503, 121593475341796875, 8255204941334951655, 605377094064557529151, 47687467918910168180223, 4015909348423983176411619

Offset: 0

Author

Peter Luschny, Dec 07 2018

Keywords

• sign

Crossrefs

Cf. A085527.

Programs

Maple

-sqrt(exp(LambertW(-x)))*(LambertW(-x) + 1): series(%, x, 32):
seq(2^n*n!*coeff(%, x, n), n=0..17);

Mathematica

a[n_] := 2^n n! SeriesCoefficient[-Sqrt[Exp[ProductLog[-x]]] (ProductLog[ -x ] + 1), {x, 0, n}]; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Jul 21 2019 *)