A376323 (1/5) times obverse convolution (3)**(2^n + 1); see Comments.

1, 6, 48, 576, 11520, 414720, 28200960, 3722526720, 967856947200, 499414184755200, 513397781928345600, 1053492248516965171200, 4319318218919557201920000, 35401132122264690826936320000, 580153753219673753271832412160000, 19012798800515148242224491811307520000

Offset: 0

Author

Clark Kimberling, Sep 20 2024

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000051, A010701, A052548, A374848, A375053, A139030.

Programs

Mathematica

s[n_] := 3; t[n_] := 2^n + 1;
u[n_] := (1/5) Product[s[k] + t[n - k], {k, 0, n}];
Table[u[n], {n, 0, 20}]
(* or *)
Table[2^(n*(n+1)/2) * QPochhammer[-4, 1/2, n+1]/5, {n, 0, 15}] (* Vaclav Kotesovec, Sep 20 2024 *)

Formula

a(n) = 2 a(n-1)*A052548(n-1) for n>=1.