A203429 a(n) = w(n+1)/(3*w(n)), where w = A203428.

-2, 27, -576, 16875, -629856, 28588707, -1528823808, 94143178827, -6561000000000, 510526328421483, -43873901280755712, 4127185885192141707, -421812572812955541504, 46542953399578857421875

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A203427, A203428.

Programs

Magma

[-(-3)^(n-1)*(n+1)^n: n in [1..20]]; // G. C. Greubel, Sep 28 2023

Mathematica

(* First program *)
f[j_]:= 1/(3*j); z = 16;
v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
1/Table[v[n], {n,z}]             (* A203428 *)
Table[v[n]/(3*v[n+1]), {n,z}]    (* A203429 *)
(* Second program *)
Table[-(-3)^(n-1)*(n+1)^n, {n,20}] (* G. C. Greubel, Sep 28 2023 *)

SageMath

[-(-3)^(n-1)*(n+1)^n for n in range(1,21)] # G. C. Greubel, Sep 28 2023

Formula

a(n) = -(-3)^(n-1) * (n+1)^n. - G. C. Greubel, Sep 28 2023