OFFSET
0,5
LINKS
Winston de Greef, Table of n, a(n) for n = 0..431
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^4/4).
E.g.f.: exp( ( -LambertW(-x^4) )^(1/4) ) / (1 + LambertW(-x^4)).
From Vaclav Kotesovec, Apr 18 2023: (Start)
a(n) ~ c * n^n / exp(3*n/4), where
c = cosh(1) + cos(1) if mod(n,4)=0,
c = sinh(1) + sin(1) if mod(n,4)=1,
c = cosh(1) - cos(1) if mod(n,4)=2,
c = sinh(1) - sin(1) if mod(n,4)=3. (End)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-x^4))^(1/4))/(1+lambertw(-x^4))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 15 2023
STATUS
approved