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

1,3

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.

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)).

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)];

Crossrefs

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

Sequence in context: A047817 A065243 A105750 * A352070 A318968 A288051

Adjacent sequences: A220446 A220447 A220448 * A220450 A220451 A220452

Keyword

sign

Author

N. J. A. Sloane, Dec 22 2012

Status

approved