OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k) * binomial(n-k,k).
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n-k, k] * (n-2*k)^(2*k), {k, 0, n/2}], {n, 1, 30}]] (* Vaclav Kotesovec, Feb 21 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^2)^(k+1)))
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^(2*k)*binomial(n-k, k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 20 2023
STATUS
approved