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)).

1, 1, -10, -1, 19, -73, 662, -2795, 281, -4511, 21746, -322921, 1035215, -720817, 1077518, -87995911, -34376687, 929280875, -92673902, 6986985769, -33833494045, 243540693677, -1817775985570, 13097400661955, -27199287430171, 8249498995171439, -112427012362483262, 3008079144099400625, -10365435567354511181

Offset: 1

Author

N. J. A. Sloane, Dec 22 2012

Keywords

• sign
• frac

Comments

Also u(n) = n*x(n-1)-1, where x(n) is defined in A220447.

Examples

			The sequence u(n) begins 1, 1, -10, -1, 19, -73/19, 662/73, -2795/331, 281/43, -4511/281, 21746/4511, ...
		

Links

• V. H. Moll, An arithmetic conjecture on a sequence of arctangent sums, 2012.

Crossrefs

Denominator(u(n)) = A220447(n-1).

Programs

Maple

A220448 := proc(n)
    if n= 1 then
        1 ;
    else
        -A105750(n)/A105750(n-1) ;
        numer(%) ;
    end if;
end proc: # R. J. Mathar, Jan 04 2013

Mathematica

x[n_] := x[n] = If[n == 1, 1, (x[n-1] + n)/(1 - n*x[n-1])];
u[n_] := If[n == 1, 1, n*x[n-1] - 1];
a[n_] := Numerator[u[n]];
Table[a[n], {n, 1, 29}] (* Jean-François Alcover, Aug 09 2023 *)