A321968 - OEIS

%I #6 Jul 21 2019 04:22:49

%S -1,3,7,55,735,13851,336743,10024911,353109375,14361853555,

%T 662358958599,34154042002983,1947046027041503,121593475341796875,

%U 8255204941334951655,605377094064557529151,47687467918910168180223,4015909348423983176411619

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

%p -sqrt(exp(LambertW(-x)))*(LambertW(-x) + 1): series(%, x, 32):

%p seq(2^n*n!*coeff(%, x, n), n=0..17);

%t 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 *)

%Y Cf. A085527.

%K sign

%O 0,2

%A _Peter Luschny_, Dec 07 2018