A376322 (1/4) times obverse convolution (2)**(2^n + 1); see Comments.

1, 5, 35, 385, 7315, 256025, 17153675, 2247131425, 582007039075, 299733625123625, 307826433001962875, 631352014087025856625, 2587911905742718986305875, 21207938067561582092776645625, 347534481113131645754330891856875, 11389052480558437163015177657041650625

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, A000079, A007395, A010701, A374848, A375054, A139030.

Programs

Mathematica

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

Formula

a(n) = a(n-1)*A062709(n) for n>=1.

a(n) = (1/4)((3)**(2^n)) = (1/4)(A010701(n)**A000079(n)) for n>=0.