%I #9 Jan 09 2024 08:45:47
%S 1,1,9,55,4289,47376,10358713,162592977,70065589761,1419907258279,
%T 1015035028009001,25173466118539344,26947505294538873409,
%U 790057195504021692521,1183327797361056503499225,40027334070963910087734751,79925496016112851520801796097
%N a(n) = Sum_{k=0..floor(n/2)} n^(3*k) * binomial(n-k,k).
%F a(n) = [x^n] 1/(1 - x - n^3*x^2).
%F 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
%t Table[Hypergeometric2F1[1/2 - n/2, -n/2, -n, -4*n^3], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 09 2024 *)
%o (PARI) a(n) = sum(k=0, n\2, n^(3*k)*binomial(n-k, k));
%Y Cf. A171180, A368888.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Jan 09 2024