1,4

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

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);

Adjacent sequences: A124263 A124264 A124265 this_sequence A124267 A124268 A124269

Sequence in context: A071299 A061380 A125567 this_sequence A137941 A077170 A079801

eigen,frac,hard,nonn

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