A124264 Hilbert-Warren Add Sequence.

2, 5, 20, 51, 312, 740, 15000, 34125, 160720, 4988592, 180774720, 844074000, 27991656000, 66264953040

Offset

1,1

Comments

Variant of A124261.

Links

Table of n, a(n) for n=1..14.

Formula

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.

Prog

(Maxima) /* [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 ] */

Crossrefs

Cf. A124261.

Sequence in context: A136897 A098510 A168541 * A274239 A271858 A189734

Adjacent sequences: A124261 A124262 A124263 * A124265 A124266 A124267

Keyword

eigen,frac,hard,nonn

Author

L. Van Warren (van(AT)wdv.com), Oct 23 2006

Extensions

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

Status

approved