A124265 Variant sequence generated by solving the order n x n linear problem [H]x = b where b is the unit vector and the sequence term is given by the denominator of the last unknown xn.

3, 3, 11, 27, 162, 380, 7650, 17325, 81340, 2518992, 91128240, 424947600, 14078156400, 33300661680, 424624548348

Offset: 1

Author

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

Keywords

• eigen
• frac
• hard
• nonn

Programs

Maxima

HilbertWarren(fun, order) := ( Unity[i,j] := 1, A : genmatrix(fun, order, order), B : genmatrix(Unity, 1, order), App : invert(triangularize(A)), Xp : App . B, 1/Xp[order] ); findWarrenSequenceTerms(fun, a, b) := ( L : append(), for order: a next order+1 through b do L: cons(first(HilbertWarren(fun,order)), L), S : reverse(L) ); k : 15; hilbert[i,j] := 1/(i + j - 1); findWarrenSequenceTerms(hilbert, 1, k); hilbertA0[i,j] := (i + j + 0)/(i + j - 1); /* sum 1 */ findWarrenSequenceTerms(hilbertA0, 1, k); hilbertA1[i,j] := (i + j + 1)/(i + j - 1); /* sum 2: there are lots of these, increment numerator */ findWarrenSequenceTerms(hilbertA1, 1, k); hilbertD1[i,j] := (i - j + 1)/(i + j - 1); /* difference 1 */ findWarrenSequenceTerms(hilbertD1, 1, k); hilbertP1[i,j] := (i * j + 0)/(i + j - 1); /* product 1 */ findWarrenSequenceTerms(hilbertP1, 1, k); hilbertQ1[i,j] := (i / j)/(i + j - 1); /* quotient 1 */ findWarrenSequenceTerms(hilbertQ1, 1, k);

Formula

[H] is defined by hilbertWarrenA1[i,j]:=(1+j+i)/(-1+j+i) where numbering starts at 1.