A368890 - OEIS

%I #8 Jan 09 2024 08:45:20

%S 1,1,65,19737,16789505,30525391000,101570840860033,558574349855881107,

%T 4722492584690006360065,58150612359276833311664895,

%U 1000009000028000035000015000001,23225285520096132372224712190010064,708804486128121003209727133170234347521

%N a(n) = Sum_{k=0..floor(n/2)} n^(3*(n-2*k)) * binomial(n-k,k).

%F a(n) = [x^n] 1/(1 - n^3*x - x^2).

%F a(n) ~ n^(3*n). - _Vaclav Kotesovec_, Jan 09 2024

%t Join[{1}, Table[n^(3*n) * Hypergeometric2F1[1/2 - n/2, -n/2, -n, -4/n^6], {n, 1, 15}]] (* _Vaclav Kotesovec_, Jan 09 2024 *)

%o (PARI) a(n) = sum(k=0, n\2, n^(3*(n-2*k))*binomial(n-k, k));

%Y Cf. A084845, A176233.

%Y Cf. A368889.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Jan 09 2024