OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..399
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x - LambertW(-x^3 * exp(3*x))/3) = ( -LambertW(-x^3 * exp(3*x))/x^3 )^(1/3).
a(n) = n! * Sum_{k=0..floor(n/3)} (1/3)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
MATHEMATICA
nmax = 20; A[_] = 1;
Do[A[x_] = Exp[x + x^3/3*A[x]^3] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3*exp(3*x))/3)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 21 2023
STATUS
approved