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A203425 a(n) = w(n+1)/(4*w(n)), where w = A203424.

%I A203425 #28 Dec 07 2023 03:03:08
%S A203425 -1,9,-128,2500,-62208,1882384,-67108864,2754990144,-128000000000,
%T A203425 6639980697856,-380420285792256,23857239165420544,
%U A203425 -1625527855624486912,119574225000000000000,-9444732965739290427392
%N A203425 a(n) = w(n+1)/(4*w(n)), where w = A203424.
%H A203425 G. C. Greubel, <a href="/A203425/b203425.txt">Table of n, a(n) for n = 1..350</a>
%F A203425 a(n) = (1/4)*(-2*(n+1))^n. - _Andrei Asinowski_, Nov 03 2015
%F A203425 E.g.f.: (1/4)*(LambertW(2*x)/(2*x*(1 + LambertW(2*x))) - 1). - _G. C. Greubel_, Dec 06 2023
%t A203425 (* First program *)
%t A203425 f[j_] := 1/(2 j); z = 16;
%t A203425 v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203425 1/Table[v[n], {n, z}]              (* A203424 *)
%t A203425 Table[v[n]/(4 v[n + 1]), {n, z}]   (* A203425 *)
%t A203425 (* Second program *)
%t A203425 Table[(-2*(n+1))^n/4, {n, 20}] (* _G. C. Greubel_, Dec 06 2023 *)
%o A203425 (PARI) for(n=1, 25, print1((1/4)*(-2*(n+1))^n, ", ")) \\ _G. C. Greubel_, Jan 28 2017
%o A203425 (Magma) [(-2*(n+1))^n/4: n in [1..20]]; // _G. C. Greubel_, Dec 06 2023
%o A203425 (SageMath) [(-2*(n+1))^n/4 for n in range(1,21)] # _G. C. Greubel_, Dec 06 2023
%Y A203425 Cf. A203424.
%K A203425 sign,easy
%O A203425 1,2
%A A203425 _Clark Kimberling_, Jan 02 2012