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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. 0
1, 1, 1, 3, 6, 10, 150, 525, 980, 24696, 740880, 2910600, 82328400, 168185160, 1870592724 (list; graph; refs; listen; history; text; internal format)
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

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: A308849 A125567 A254957 * A137941 A077170 A083462

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

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Last modified July 22 15:23 EDT 2019. Contains 325224 sequences. (Running on oeis4.)