OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..465
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^4/24).
E.g.f.: exp( ( -6*LambertW(-x^4/6) )^(1/4) ) / (1 + LambertW(-x^4/6)).
MATHEMATICA
nmax = 30; CoefficientList[PowerExpand[Series[E^((-6*LambertW[-x^4/6])^(1/4)) / (1 + LambertW[-x^4/6]), {x, 0, nmax}]], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 18 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-6*lambertw(-x^4/6))^(1/4))/(1+lambertw(-x^4/6))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 16 2023
STATUS
approved