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

%I A220449 #17 May 23 2014 11:14:37
%S A220449 1,1,-10,10,190,-730,-6620,55900,365300,-5864300,-28269800,839594600,
%T A220449 2691559000,-159300557000,-238131478000,38894192662000,
%U A220449 -15194495654000,-11911522255750000,29697351895900000,4477959179352100000,-21683886333440500000,-2029107997508660900000,15145164178973569000000
%N A220449 Define u(n) as in A220448; then a(1)=1, thereafter a(n) = u(n)*a(n-1).
%C A220449 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).
%H A220449 N. J. A. Sloane, <a href="/A220449/b220449.txt">Table of n, a(n) for n = 1..100</a>
%H A220449 V. H. Moll, <a href="http://www.tulane.edu/~vhm/papers_html/xn-final.pdf">An arithmetic conjecture on a sequence of arctangent sums</a>, 2012. See f_n.
%F A220449 A105750(n) = (-1)^(n+1)*a(n).
%F A220449 Define x(n) as in A220447. Then x(n) = (a(n+1)+a(n))/((n+1)*a(n)).
%p A220449 x:=proc(n) option remember;
%p A220449 if n=1 then 1 else (x(n-1)+n)/(1-n*x(n-1)); fi; end;
%p A220449 f:=proc(n) option remember; global x;
%p A220449 if n = 1 then 1 else n*x(n-1)*f(n-1)-f(n-1); fi; end;
%p A220449 [seq(f(n),n=1..30)];
%Y A220449 Cf. A105750, A220446, A220447, A220448, A220450, A220451.
%K A220449 sign
%O A220449 1,3
%A A220449 _N. J. A. Sloane_, Dec 22 2012