A374866 Obverse convolution (n)**(3n+2); see Comments.

2, 15, 192, 3465, 80640, 2297295, 77414400, 3011753745, 132843110400, 6550564395375, 357082280755200, 21322087106945625, 1384050920207155200, 97036818423709539375, 7307788858693779456000, 588334230102950937230625, 50423743124987078246400000

Offset: 0

Author

Clark Kimberling, Aug 28 2024

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000027, A016789, A374848.

Programs

Mathematica

s[n_] := n; t[n_] := 3 n + 2;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]
(* or *)
Table[2^n*(n+2)*Pochhammer[2 + n/2, n], {n, 0, 20}] (* Vaclav Kotesovec, Aug 28 2024 *)

Formula

a(n) ~ 3^(3*(n+1)/2) * n^(n+1) / exp(n). - Vaclav Kotesovec, Aug 28 2024