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Search: id:A107254
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| A107254 |
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SF(2n-1)/SF(n-1)^2 where SF is the superfactorial A000178 product of factorials. |
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3
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| 1, 1, 12, 8640, 870912000, 22122558259200000, 222531556847250309120000000, 1280394777025250130271722799104000000000, 5746332926632566442385615219551212618645504000000000000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Inverse product of all matrix elements of n X n Hilbert Matrix M(i,j) = 1/(i+j-1) (i,j = 1..n). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = n!*(n+1)!*(n+2)!*...*(2n-1)!/(0!*1!*2!*3!*...*(n-1)!) = A000178(2n-1)/A000178(n-1)^2 = A079478(n)/A000984(n) = A079478(n-1)*A009445(n-1) = A107252(n)*A000142(n) = A088020(n)/A039622(n).
a(n) = 1/Product[Product[1/(i+j-1),{i,1,n}],{j,1,n}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
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EXAMPLE
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a(3) = 1!*2!*3!*4!*5!/(1!*2!*1!*2!) = 34560/4 = 8640.
n = 2: HilbertMatrix[n,n]
1 1/2
1/2 1/3
so a(2) = 1 / (1 * 1/2 * 1/2 * 1/3) = 12.
The n X n Hilbert matrix begins:
1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 ...
1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 ...
1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 ...
1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 ...
1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12 ...
1/6 1/7 1/8 1/9 1/10 1/11 1/12 1/13 ...
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MATHEMATICA
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Table[Product[Product[(i+j-1), {i, 1, n}], {j, 1, n}], {n, 1, 10}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
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CROSSREFS
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Cf. A002457.
Cf. A098118, A005249.
Sequence in context: A013481 A013513 A013480 this_sequence A012532 A012732 A001322
Adjacent sequences: A107251 A107252 A107253 this_sequence A107255 A107256 A107257
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 14 2005
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