OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..392
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x - LambertW(-3*x^2/2 * exp(x))) = -2 * LambertW(-3*x^2/2 * exp(x))/(3*x^2).
a(n) = n! * Sum_{k=0..floor(n/2)} (3/2)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).
MATHEMATICA
nmax = 20; A[_] = 1;
Do[A[x_] = Exp[x + 3*x^2/2*A[x]] + 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(-3*x^2/2*exp(x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 20 2023
STATUS
approved