A374889 Obverse convolution (n^2)**(2n-1); see Comments.

1, 6, 100, 2940, 132192, 8368360, 705938688, 76289850000, 10252702720000, 1674156061141344, 326009771116646400, 74554986880418359744, 19767651264345600000000, 6010708728599919162000000, 2076396132003401567272173568, 808279585896351070399895712000

Offset: 0

Author

Clark Kimberling, Sep 14 2024

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000290, A005408, A374848.

Programs

Mathematica

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

Formula

a(n) ~ 2^(3/2) * n^(2*n + 1/2) / exp(2*n + 2 - Pi*sqrt(2*n)). - Vaclav Kotesovec, Sep 15 2024