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Search: id:A069651
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| A069651 |
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For n >= 1, let M_n be the n X n matrix with M_n(i,j)=i^2/(i+j); then a(n)=1/det(M_n). Also a(0) = 1 by convention. |
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2
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| 1, 2, 18, 1200, 735000, 4667544000, 332086420512000, 279394363051195392000, 2892376010829659126572800000, 379850021025259936655866602240000000, 648304836222110631242066578424390188032000000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also, determinant of the inverse of the (n+1)-st Hilbert matrix, divided by (2n+1)!. - Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 02 2004
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FORMULA
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a(n) = A005249(n)/A000142(n). - Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 02 2004
a(n) = (n+1)!/(2*n+1)! * Product[Binomial(i,Floor(i/2)), {i,1,2*n+1}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 26 2008
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MATHEMATICA
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Table[1/((2n - 1)!Det[Table[1/(i + j - 1), {i, n}, {j, n}]]), {n, 10}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 02 2004
Table[(n + 1)!/(2*n + 1)!*Product[Binomial[i, Floor[i/2]], {i, 1, 2*n + 1}], {n, 0, 10}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 26 2008
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PROGRAM
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(PARI) for(n=1, 15, print1(1/matdet(matrix(n, n, i, j, i^2/(j+i))), ", "))
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CROSSREFS
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Sequence in context: A013040 A139111 A090766 this_sequence A123558 A076954 A060598
Adjacent sequences: A069648 A069649 A069650 this_sequence A069652 A069653 A069654
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2002
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EXTENSIONS
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Edited by njas, Feb 25 2008
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