A368889 a(n) = Sum_{k=0..floor(n/2)} n^(3*k) * binomial(n-k,k).
1, 1, 9, 55, 4289, 47376, 10358713, 162592977, 70065589761, 1419907258279, 1015035028009001, 25173466118539344, 26947505294538873409, 790057195504021692521, 1183327797361056503499225, 40027334070963910087734751, 79925496016112851520801796097
Offset: 0
Programs
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Mathematica
Table[Hypergeometric2F1[1/2 - n/2, -n/2, -n, -4*n^3], {n, 0, 20}] (* Vaclav Kotesovec, Jan 09 2024 *) -
PARI
a(n) = sum(k=0, n\2, n^(3*k)*binomial(n-k, k));
Formula
a(n) = [x^n] 1/(1 - x - n^3*x^2).
a(n) ~ n^(3*n/2) if n is even and a(n) ~ n^((3*n-1)/2)/2 if n is odd. - Vaclav Kotesovec, Jan 09 2024