OFFSET
0,4
LINKS
Robert Israel, Table of n, a(n) for n = 0..403
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x - LambertW(x^2 * exp(2*x))/2) = sqrt( LambertW(x^2 * exp(2*x))/x^2 ).
a(n) = n! * Sum_{k=0..floor(n/2)} (-1/2)^k * (2*k+1)^(n-k-1) / (k! * (n-2*k)!).
MAPLE
N:= 50: # for a(0)..a(N)
egf:= exp(x - LambertW(x^2 * exp(2*x))/2):
S:=series(egf, x, N+1):
[seq](coeff(S, x, i)*i!, i=0..N); # Robert Israel, May 22 2023
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^2*exp(2*x))/2)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 22 2023
STATUS
approved