A375058 (1/4)*(obverse convolution (n^2 + n)**(n^2 + n)); see Comments.

0, 1, 36, 2304, 235200, 35283600, 7326498816, 2014310301696, 708764628418560, 310741583364000000, 166127945369278464000, 106393998792968997175296, 80420536739705661368303616, 70845563326799184430297190400, 71952548266212946033508352000000

Offset: 0

Author

Clark Kimberling, Sep 22 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; (sqrt(a(2k+1))) = (1, 48, 5940, 1419264, 557442000, 326180929536, ...).

Crossrefs

Cf. A374848.

Programs

Mathematica

s[n_] := n^2 + n; t[n_] := n^2 + n;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}];
Table[u[n]/4, {n, 0, 20}]

Formula

a(n) ~ n^(2*n+2) / (4*exp(2*n - Pi*(n+1)/2)). - Vaclav Kotesovec, Sep 22 2024