A375051 Obverse convolution (n^2 - 1)**(n^2 - 1); see Comments.

-2, 1, 0, 441, 75264, 14402025, 3451797504, 1043554187025, 392874877255680, 181193143212358641, 100757479882752000000, 66592039534109652160521, 51648427918242896412672000, 46486269540273907302519872025, 48078115878910207012782666153984

Offset: 0

Author

Clark Kimberling, Sep 15 2024

Keywords

• sign

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

a(2k+1) is a square for k>=0.

Crossrefs

Cf. A005563, A323540, A374848, A375052.

Programs

Mathematica

s[n_] := n^2 - 1; t[n_] := n^2 - 1;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}];
Table[u[n], {n, 0, 20}]

Formula

a(n) ~ n^(2*n+2) / exp(2*n - Pi*n/2). - Vaclav Kotesovec, Sep 19 2024