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

%I A203427 #24 Dec 05 2023 08:34:19
%S A203427 -3,48,-1000,25920,-806736,29360128,-1224440064,57600000000,
%T A203427 -3018173044480,174359297654784,-11011033460963328,754709361539940352,
%U A203427 -55801305000000000000,4427218577690292387840,-375183514207494575620096,33824309717272203758665728,-3232463698006063164519284736,326417514496000000000000000000
%N A203427 a(n) = w(n+1)/(4*w(n)), where w = A203426.
%H A203427 G. C. Greubel, <a href="/A203427/b203427.txt">Table of n, a(n) for n = 1..345</a>
%F A203427 a(n) = (1/4) * (n+1) * (-2*(n+2))^n. - _Andrei Asinowski_, Nov 03 2015
%t A203427 (* First program *)
%t A203427 f[j_]:= 1/(2 j + 2); z = 12;
%t A203427 v[n_]:= Product[Product[f[k] - f[j], {j, k-1}], {k, 2, n}];
%t A203427 1/Table[v[n], {n, z}]               (* A203426 *)
%t A203427 Table[v[n]/(4 v[n + 1]), {n, z}]    (* A203427 *)
%t A203427 (* Second program *)
%t A203427 Table[(-2*(n+2))^n*(n+1)/4, {n,20}] (* _G. C. Greubel_, Dec 05 2023 *)
%o A203427 (Magma) [(-2*(n+2))^n*(n+1)/4: n in [1..20]]; // _G. C. Greubel_, Dec 05 2023
%o A203427 (SageMath) [(-2*(n+2))^n*(n+1)/4 for n in range(1,21)] # _G. C. Greubel_, Dec 05 2023
%Y A203427 Cf. A203425, A203426.
%K A203427 sign
%O A203427 1,1
%A A203427 _Clark Kimberling_, Jan 02 2012
%E A203427 Name corrected by _Andrei Asinowski_, Nov 03 2015
%E A203427 Terms a(14) onward added by _G. C. Greubel_, Dec 05 2023