A368888 a(n) = Sum_{k=0..floor(n/2)} n^(2*k) * binomial(n-k,k).
1, 1, 5, 19, 305, 1976, 54613, 494901, 19460545, 226000855, 11535280901, 163226844144, 10246715573041, 170910034261721, 12736193619206485, 244588264748170651, 21100437309369290497, 458426839205360652760, 44935948904379592796101
Offset: 0
Programs
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Mathematica
Table[Hypergeometric2F1[1/2 - n/2, -n/2, -n, -4*n^2], {n, 0, 20}] (* Vaclav Kotesovec, Jan 09 2024 *) -
PARI
a(n) = sum(k=0, n\2, n^(2*k)*binomial(n-k, k));
Formula
a(n) = [x^n] 1/(1 - x - (n*x)^2).
a(n) ~ (exp(1/2) + (-1)^n*exp(-1/2)) * n^n / 2. - Vaclav Kotesovec, Jan 09 2024