A375059 Obverse convolution (n^2 + n + 1)**(n^2 + n + 1); see Comments.

2, 16, 384, 19600, 1734656, 235929600, 45619718144, 11882195067136, 4007380608000000, 1698030663170523136, 882712840220180480000, 552231274155798665465856, 409206182467603556470882304, 354386995669969036902400000000, 354633184176852764825029617647616

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, 35, 3840, 861764, 325771264, 185780662704...).

Crossrefs

Cf. A374848, A375058.

Programs

Mathematica

s[n_] := n^2 + n + 1; t[n_] := n^2 + n + 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+1)/2). - Vaclav Kotesovec, Sep 22 2024