%I #3 Mar 30 2012 16:50:35
%S 2,5,20,51,312,740,15000,34125,160720,4988592,180774720,844074000,
%T 27991656000,66264953040
%N HilbertWarren Add Sequence.
%C Variant of A124261.
%F Terms generated by solving n x n linear system [H']x = b where b is unity and elements of H' are given by H'[i,j] = (i + j)/(i + j  1). Sequence term is the denominator of last unknown xn. Numerator is unity for last term for all problem orders examined.
%o /* [wxMaxima: input start ] */ load("eigen"); order : 4; X : columnvector(makelist(concat(x,i), i, 1, order)); h[i,j] := (i + j)/(i + j  1); Unity[i,j] := 1; A : genmatrix(h, order, order); A . X; B : genmatrix(Unity, 1, order); A . X = B; Ap : triangularize(A); Ap . X = B; App : invert(Ap); App . B; /* [wxMaxima: input end ] */
%Y Cf. A124261.
%K eigen,frac,hard,nonn
%O 1,1
%A L. Van Warren (van(AT)wdv.com), Oct 23 2006
%E The author said that this version of the submission was unsatisfactory and set me a better version in email, which may replace this.  _N. J. A. Sloane_, Oct 24 2006
