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

-1, 9, -128, 2500, -62208, 1882384, -67108864, 2754990144, -128000000000, 6639980697856, -380420285792256, 23857239165420544, -1625527855624486912, 119574225000000000000, -9444732965739290427392

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..350

Crossrefs

Cf. A203424.

Programs

Magma

[(-2*(n+1))^n/4: n in [1..20]]; // G. C. Greubel, Dec 06 2023

Mathematica

(* First program *)
f[j_] := 1/(2 j); z = 16;
v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
1/Table[v[n], {n, z}]              (* A203424 *)
Table[v[n]/(4 v[n + 1]), {n, z}]   (* A203425 *)
(* Second program *)
Table[(-2*(n+1))^n/4, {n, 20}] (* G. C. Greubel, Dec 06 2023 *)

PARI

for(n=1, 25, print1((1/4)*(-2*(n+1))^n, ", ")) \\ G. C. Greubel, Jan 28 2017

SageMath

[(-2*(n+1))^n/4 for n in range(1,21)] # G. C. Greubel, Dec 06 2023

Formula

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

E.g.f.: (1/4)*(LambertW(2*x)/(2*x*(1 + LambertW(2*x))) - 1). - G. C. Greubel, Dec 06 2023