OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..322
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: ( -LambertW(-3*x*exp(3*x)) / (3*x) )^(1/3) = exp( x - LambertW(-3*x*exp(3*x))/3 ).
a(n) = Sum_{k=0..n} (3*k+1)^(n-1) * binomial(n,k) = 2^n * A349714(n).
a(n) ~ sqrt(LambertW(exp(-1)) + 1) * 3^(n-1) * n^(n-1) / (exp(n) * LambertW(exp(-1))^(n + 1/3)). - Vaclav Kotesovec, Apr 24 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x*exp(3*x))/3)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 01 2023
STATUS
approved