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Obverse convolution (n)**(3n+2); see Comments.
1

%I #7 Sep 11 2024 13:35:51

%S 2,15,192,3465,80640,2297295,77414400,3011753745,132843110400,

%T 6550564395375,357082280755200,21322087106945625,1384050920207155200,

%U 97036818423709539375,7307788858693779456000,588334230102950937230625,50423743124987078246400000

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

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

%F a(n) ~ 3^(3*(n+1)/2) * n^(n+1) / exp(n). - _Vaclav Kotesovec_, Aug 28 2024

%t s[n_] := n; t[n_] := 3 n + 2;

%t u[n_] := Product[s[k] + t[n - k], {k, 0, n}]

%t Table[u[n], {n, 0, 20}]

%t (* or *)

%t Table[2^n*(n+2)*Pochhammer[2 + n/2, n], {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 28 2024 *)

%Y Cf. A000027, A016789, A374848.

%K nonn

%O 0,1

%A _Clark Kimberling_, Aug 28 2024