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Search: id:A069640
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| A069640 |
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Let M_n be the n X n matrix with M_n(i,j)=1/(i+j+1); then a(n)=1/det(M_n). |
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| 3, 240, 378000, 10668672000, 5175372787200000, 42202225467872870400000, 5708700736339601341845504000000, 12701009683686045652926579789004800000000, 462068939479146913162956288390362787269836800000000
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Wolfram Research, 1991 Mathematica Conference, Elementary Tutorial Notes, Section 1, Introduction to Mathematica, Paul Abbott, page1 9.
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FORMULA
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a(n) = (2*n+1)!!*(n!*Product[(2*k)!/k!/(k+1)!,{k,0,n}])^2. a(n) = (2*n+1)!!*(n!*A003046(n))^2, where A003046(n)is the Product of first n Catalan numbers A000108(n). a(n) = (2*n+1)!*n!/(2^n)*A003046(n)^2. - Alexander Adamchuk (alex(AT)kolmogorov.com), May 17 2006
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MATHEMATICA
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Hilbert[n_Integer] := Table[1/(i + j + 1), {i, n}, {j, n}]; Table[ 1 / Det[ Hilbert[n]], {n, 1, 8}] (from Robert G. Wilson v Mar 13 2004)
Table[(2*n+1)!!*(n!*Product[(2*k)!/k!/(k+1)!, {k, 0, n}])^2, {n, 1, 11}] - Alexander Adamchuk (alex(AT)kolmogorov.com), May 17 2006
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PROGRAM
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(PARI) for(n=1, 10, print1(1/matdet(matrix(n, n, i, j, 1/(i+j+1))), ", "))
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CROSSREFS
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Cf. A000108, A003046, A005249, A067689.
Sequence in context: A053970 A103062 A024044 this_sequence A013778 A092799 A140163
Adjacent sequences: A069637 A069638 A069639 this_sequence A069641 A069642 A069643
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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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