%I #24 Dec 05 2023 08:34:19

%S -3,48,-1000,25920,-806736,29360128,-1224440064,57600000000,

%T -3018173044480,174359297654784,-11011033460963328,754709361539940352,

%U -55801305000000000000,4427218577690292387840,-375183514207494575620096,33824309717272203758665728,-3232463698006063164519284736,326417514496000000000000000000

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

%H G. C. Greubel, <a href="/A203427/b203427.txt">Table of n, a(n) for n = 1..345</a>

%F a(n) = (1/4) * (n+1) * (-2*(n+2))^n. - _Andrei Asinowski_, Nov 03 2015

%t (* First program *)

%t f[j_]:= 1/(2 j + 2); z = 12;

%t v[n_]:= Product[Product[f[k] - f[j], {j, k-1}], {k, 2, n}];

%t 1/Table[v[n], {n, z}] (* A203426 *)

%t Table[v[n]/(4 v[n + 1]), {n, z}] (* A203427 *)

%t (* Second program *)

%t Table[(-2*(n+2))^n*(n+1)/4, {n,20}] (* _G. C. Greubel_, Dec 05 2023 *)

%o (Magma) [(-2*(n+2))^n*(n+1)/4: n in [1..20]]; // _G. C. Greubel_, Dec 05 2023

%o (SageMath) [(-2*(n+2))^n*(n+1)/4 for n in range(1,21)] # _G. C. Greubel_, Dec 05 2023

%Y Cf. A203425, A203426.

%K sign

%O 1,1

%A _Clark Kimberling_, Jan 02 2012

%E Name corrected by _Andrei Asinowski_, Nov 03 2015

%E Terms a(14) onward added by _G. C. Greubel_, Dec 05 2023