A124266 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.

1, 1, 1, 3, 6, 10, 150, 525, 980, 24696, 740880, 2910600, 82328400, 168185160, 1870592724

Offset

1,4

Links

Table of n, a(n) for n=1..15.

Formula

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

Prog

(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);

Crossrefs

Sequence in context: A368173 A125567 A254957 * A137941 A353998 A355181

Adjacent sequences: A124263 A124264 A124265 * A124267 A124268 A124269

Keyword

eigen,frac,hard,nonn

Author

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

Status

approved