A203427 a(n) = w(n+1)/(4*w(n)), where w = A203426.

-3, 48, -1000, 25920, -806736, 29360128, -1224440064, 57600000000, -3018173044480, 174359297654784, -11011033460963328, 754709361539940352, -55801305000000000000, 4427218577690292387840, -375183514207494575620096, 33824309717272203758665728, -3232463698006063164519284736, 326417514496000000000000000000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 1..345

Crossrefs

Cf. A203425, A203426.

Programs

Magma

[(-2*(n+2))^n*(n+1)/4: n in [1..20]]; // G. C. Greubel, Dec 05 2023

Mathematica

(* First program *)
f[j_]:= 1/(2 j + 2); z = 12;
v[n_]:= Product[Product[f[k] - f[j], {j, k-1}], {k, 2, n}];
1/Table[v[n], {n, z}]               (* A203426 *)
Table[v[n]/(4 v[n + 1]), {n, z}]    (* A203427 *)
(* Second program *)
Table[(-2*(n+2))^n*(n+1)/4, {n,20}] (* G. C. Greubel, Dec 05 2023 *)

SageMath

[(-2*(n+2))^n*(n+1)/4 for n in range(1,21)] # G. C. Greubel, Dec 05 2023

Formula

a(n) = (1/4) * (n+1) * (-2*(n+2))^n. - Andrei Asinowski, Nov 03 2015

Extensions

Name corrected by Andrei Asinowski, Nov 03 2015

Terms a(14) onward added by G. C. Greubel, Dec 05 2023