OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..393
FORMULA
E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^3)).
a(n) ~ sqrt(Pi/3) * exp((2*n - 3)/(6*LambertW(exp(1/4)*(2*n - 3)/8)) - 4*n/3) * n^(4*n/3 + 1/2) / (sqrt(1 + LambertW(exp(1/4)*(2*n - 3)/8)) * 2^(2*n/3 + 1/2) * LambertW(exp(1/4)*(2*n - 3)/8)^(n/3)). - Vaclav Kotesovec, Nov 01 2022
MATHEMATICA
a[n_] := n! * Sum[(n - 3*k)^k/(n - 3*k)!, {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(n-3*k)!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^3)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 18 2022
STATUS
approved