OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..350
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
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 *)
PROG
(PARI) for(n=1, 25, print1((1/4)*(-2*(n+1))^n, ", ")) \\ G. C. Greubel, Jan 28 2017
(Magma) [(-2*(n+1))^n/4: n in [1..20]]; // G. C. Greubel, Dec 06 2023
(SageMath) [(-2*(n+1))^n/4 for n in range(1, 21)] # G. C. Greubel, Dec 06 2023
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Clark Kimberling, Jan 02 2012
STATUS
approved