OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..366
FORMULA
E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^2)).
a(n) ~ sqrt(Pi) * exp((n-1)/(2*LambertW(exp(1/3)*(n-1)/3)) - 3*n/2) * n^((3*n + 1)/2) / (sqrt(1 + LambertW(exp(1/3)*(n - 1)/3)) * 3^((n+1)/2) * LambertW(exp(1/3)*(n-1)/3)^(n/2)). - Vaclav Kotesovec, Nov 01 2022
MATHEMATICA
a[n_] := n! * Sum[(n - 2*k)^k/(n - 2*k)!, {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 21, 0] (* Amiram Eldar, Aug 19 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(n-2*k)!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^2)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 18 2022
STATUS
approved