OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..315
FORMULA
E.g.f.: Sum_{k>=0} x^(2*k) / (k! * (1 - k * x)).
a(n) ~ sqrt(2*Pi) * exp((n - 1/2)/LambertW(exp(2/3)*(2*n - 1)/6) - 2*n) * n^(2*n + 1/2) / (3^(n + 1/2) * sqrt(1 + LambertW(exp(2/3)*(2*n - 1)/6)) * LambertW(exp(2/3)*(2*n - 1)/6)^n). - Vaclav Kotesovec, Oct 30 2022
MATHEMATICA
Join[{1}, Table[n!*Sum[k^(n - 2*k)/k!, {k, 0, n/2}], {n, 1, 20}]] (* Vaclav Kotesovec, Oct 30 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^(2*k)/(k!*(1-k*x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 17 2022
STATUS
approved