A374878 Obverse convolution (3n+2)**(3n+2); see Comments.

4, 49, 1000, 28561, 1048576, 47045881, 2494357888, 152587890625, 10578455953408, 819628286980801, 70188843638032384, 6582952005840035281, 671088640000000000000, 73885357344138503765449, 8737103395697172336050176, 1104427674243920646305299201

Offset: 0

Author

Clark Kimberling, Sep 13 2024

Keywords

• nonn
• easy

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. A016789, A374848, A374877.

Programs

Mathematica

s[n_] := 3 n + 2; t[n_] := 3 n + 2;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 17}]
(* or *)
Table[(3*n+4)^(n+1), {n,0,20}] (* Vaclav Kotesovec, Sep 13 2024 *)

Formula

From Vaclav Kotesovec, Sep 13 2024: (Start)

a(n) = (3*n+4)^(n+1).

a(n) ~ exp(4/3) * 3^(n+1) * n^(n+1). (End)