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