A376324 (1/6) times obverse convolution (4)**(2^n + 1); see Comments.

1, 7, 63, 819, 17199, 636363, 43909047, 5839903251, 1524214748511, 788019024980187, 810871576704612423, 1664719346974569304419, 6827014041942708717422319, 55961034101804383356710748843, 917145387894472038833132462787927

Offset: 0

Author

Clark Kimberling, Sep 20 2024

Keywords

• nonn

References

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

Crossrefs

Cf. A000051, A010709, A168614, A374848, A375053, A375054.

Programs

Mathematica

s[n_] := 4; t[n_] := 2^n + 1;
u[n_] := (1/6) Product[s[k] + t[n - k], {k, 0, n}];
Table[u[n], {n, 0, 20}]
(* or *)
Table[2^(n*(n+1)/2 - 1) * QPochhammer[-5, 1/2, n+1]/3, {n, 0, 15}] (* Vaclav Kotesovec, Sep 20 2024 *)

Formula

a(n) = a(n-1)*A168614(n) for n>=1.