A374879 Obverse convolution (n)**(floor(3n/2)); see Comments.

0, 1, 12, 144, 2400, 44100, 1016064, 25401600, 752716800, 23851713600, 865728864000, 33243988377600, 1429216756531200, 64493406138470400, 3205589417533440000, 166232708366376960000, 9379957624086763929600, 549606892036333824000000, 34710813126114757632000000

Offset: 0

Author

Clark Kimberling, Sep 13 2024

Keywords

• nonn

Comments

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

If k>=0, then a(2k+1) is a square.

Crossrefs

Cf. A000027, A016789, A374848.

Programs

Mathematica

s[n_] := n; t[n_] := Floor[3 n/2];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 24}]

Formula

a(n) ~ 3^(3*n) * n^(n+1) / (2^(3*n) * exp(n)). - Vaclav Kotesovec, Sep 13 2024