A376321 Obverse convolution (n^2 + 1)**(n^2 + 1); see Comments.

2, 9, 144, 5929, 466560, 59213025, 10958689280, 2771535732849, 915539439919104, 382088350057032025, 196357891384811520000, 121752085389995771825625, 89582478947424173216497664, 77138638421388109999960896369, 76829768389915556918132736000000

Offset: 0

Author

Clark Kimberling, Sep 20 2024

Keywords

• nonn

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. A323540, A374848, A375051.

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 20 2024