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

2, 25, 512, 14641, 537824, 24137569, 1280000000, 78310985281, 5429503678976, 420707233300201, 36028797018963968, 3379220508056640625, 344498040522809827328, 37929227194915558802161, 4485286068729022118887424, 566977372488557307219621121

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) is even and a(2k+1) is a square.

Crossrefs

Cf. A016777, A374848, A374878.

Programs

Mathematica

s[n_] := 3 n + 1; t[n_] := 3 n + 1;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 17}]
(* or *)
Table[(3*n+2)^(n+1), {n,0,20}] (* Vaclav Kotesovec, Sep 13 2024 *)

Formula

From Vaclav Kotesovec, Sep 13 2024: (Start)

a(n) = (3*n+2)^(n+1).

a(n) ~ exp(2/3) * 3^(n+1) * n^(n+1). (End)