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