A203423 a(n) = w(n+1)/(2*w(n)), where w=A203422.

-3, 24, -250, 3240, -50421, 917504, -19131876, 450000000, -11789738455, 340545503232, -10752962364222, 368510430439424, -13623365478515625, 540431955284459520, -22899384412078526344, 1032236014321051140096, -49323481720063219673451, 2490368000000000000000000, -132484966403310261255807810

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• sign

Links

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

Crossrefs

Cf. A000169, A053506, A203421, A203422.

Programs

Magma

[(-1)^n*(n+1)*(n+2)^n/2: n in [1..20]]; // G. C. Greubel, Dec 07 2023

Mathematica

(* First program *)
f[j_] := 1/(j + 1); z = 16;
v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
1/Table[v[n], {n, 1, z}]             (* A203422 *)
Table[v[n]/(2 v[n + 1]), {n, 1, z}]  (* this sequence *)
(* Second program *)
Table[(-1)^n*(n+1)*(n+2)^n/2, {n,20}] (* G. C. Greubel, Dec 07 2023 *)

SageMath

[(-1)^n*(n+1)*(n+2)^n/2 for n in range(1,21)] # G. C. Greubel, Dec 07 2023

Formula

a(n) = (-1)^n*A053506(n+2)/2. - Steven Finch, Apr 16 2022

E.g.f.: -(1/(2*x^2))*( W(x)/(1 + W(x))^3 - 2*W(x)/(1 + W(x)) + W(x) + x^2), where W(x) = LambertW(x). - G. C. Greubel, Dec 07 2023