OFFSET
0,2
LINKS
Winston de Greef, Table of n, a(n) for n = 0..338
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = (-1)^n * n! * Sum_{k=0..n} (-3)^k * (k+1)^(k-1) * binomial(n-1,n-k)/k!.
E.g.f.: exp ( -LambertW(-3*x/(1+x)) ).
E.g.f.: -(1+x)/(3*x) * LambertW(-3*x/(1+x)).
MATHEMATICA
Table[(-1)^n*n!*Sum[(-3)^k*(k + 1)^(k - 1)*Binomial[n - 1, n - k]/k!, {k, 0, n}], {n, 0, 20}] (* Wesley Ivan Hurt, May 25 2024 *)
PROG
(PARI) a(n) = (-1)^n*n!*sum(k=0, n, (-3)^k*(k+1)^(k-1)*binomial(n-1, n-k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x/(1+x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1+x)/(3*x)*lambertw(-3*x/(1+x))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 04 2023
STATUS
approved