A220449 Define u(n) as in A220448; then a(1)=1, thereafter a(n) = u(n)*a(n-1).

1, 1, -10, 10, 190, -730, -6620, 55900, 365300, -5864300, -28269800, 839594600, 2691559000, -159300557000, -238131478000, 38894192662000, -15194495654000, -11911522255750000, 29697351895900000, 4477959179352100000, -21683886333440500000, -2029107997508660900000, 15145164178973569000000

Offset: 1

Author

N. J. A. Sloane, Dec 22 2012

Keywords

• sign

Comments

The reason for including this sequence as well as A105750 is that the values of this sequence modulo various primes are of interest (see Moll).

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..100
• V. H. Moll, An arithmetic conjecture on a sequence of arctangent sums, 2012. See f_n.

Crossrefs

Cf. A105750, A220446, A220447, A220448, A220450, A220451.

Programs

Maple

x:=proc(n) option remember;
if n=1 then 1 else (x(n-1)+n)/(1-n*x(n-1)); fi; end;
f:=proc(n) option remember; global x;
if n = 1 then 1 else n*x(n-1)*f(n-1)-f(n-1); fi; end;
[seq(f(n),n=1..30)];

Formula

A105750(n) = (-1)^(n+1)*a(n).

Define x(n) as in A220447. Then x(n) = (a(n+1)+a(n))/((n+1)*a(n)).