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A220448 Define a sequence u(n) by u(1)=1; thereafter u(n) = f(n)/f(n-1) where f(n) = (-1)^(n+1)*A105750(n); sequence gives numerator(u(n)).

%I A220448 #13 Aug 09 2023 12:39:23
%S A220448 1,1,-10,-1,19,-73,662,-2795,281,-4511,21746,-322921,1035215,-720817,
%T A220448 1077518,-87995911,-34376687,929280875,-92673902,6986985769,
%U A220448 -33833494045,243540693677,-1817775985570,13097400661955,-27199287430171,8249498995171439,-112427012362483262,3008079144099400625,-10365435567354511181
%N A220448 Define a sequence u(n) by u(1)=1; thereafter u(n) = f(n)/f(n-1) where f(n) = (-1)^(n+1)*A105750(n); sequence gives numerator(u(n)).
%C A220448 Also u(n) = n*x(n-1)-1, where x(n) is defined in A220447.
%H A220448 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.
%e A220448 The sequence u(n) begins 1, 1, -10, -1, 19, -73/19, 662/73, -2795/331, 281/43, -4511/281, 21746/4511, ...
%p A220448 A220448 := proc(n)
%p A220448     if n= 1 then
%p A220448         1 ;
%p A220448     else
%p A220448         -A105750(n)/A105750(n-1) ;
%p A220448         numer(%) ;
%p A220448     end if;
%p A220448 end proc: # _R. J. Mathar_, Jan 04 2013
%t A220448 x[n_] := x[n] = If[n == 1, 1, (x[n-1] + n)/(1 - n*x[n-1])];
%t A220448 u[n_] := If[n == 1, 1, n*x[n-1] - 1];
%t A220448 a[n_] := Numerator[u[n]];
%t A220448 Table[a[n], {n, 1, 29}] (* _Jean-François Alcover_, Aug 09 2023 *)
%Y A220448 Denominator(u(n)) = A220447(n-1).
%K A220448 sign,frac
%O A220448 1,3
%A A220448 _N. J. A. Sloane_, Dec 22 2012