cp's OEIS Frontend

A374877 Obverse convolution (3n+1)**(3n+1); see Comments.

%I A374877 #11 Sep 16 2024 14:25:42
%S A374877 2,25,512,14641,537824,24137569,1280000000,78310985281,5429503678976,
%T A374877 420707233300201,36028797018963968,3379220508056640625,
%U A374877 344498040522809827328,37929227194915558802161,4485286068729022118887424,566977372488557307219621121
%N A374877 Obverse convolution (3n+1)**(3n+1); see Comments.
%C A374877 See A374848 for the definition of obverse convolution and a guide to related sequences.
%C A374877 If k>=0, then a(2k) is even and a(2k+1) is a square.
%F A374877 From _Vaclav Kotesovec_, Sep 13 2024: (Start)
%F A374877 a(n) = (3*n+2)^(n+1).
%F A374877 a(n) ~ exp(2/3) * 3^(n+1) * n^(n+1). (End)
%t A374877 s[n_] := 3 n + 1; t[n_] := 3 n + 1;
%t A374877 u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
%t A374877 Table[u[n], {n, 0, 17}]
%t A374877 (* or *)
%t A374877 Table[(3*n+2)^(n+1), {n,0,20}] (* _Vaclav Kotesovec_, Sep 13 2024 *)
%Y A374877 Cf. A016777, A374848, A374878.
%K A374877 nonn
%O A374877 0,1
%A A374877 _Clark Kimberling_, Sep 13 2024