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Search: id:A108078
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| A108078 |
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Determinant of a Hankel matrix with factorial elements. |
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+0
1
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| 2, 12, 576, 414720, 7166361600, 4334215495653800, 125824009529730280000000, 230121443464257970000000000000000, 33669808618214310000000000000000000000000000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The first term (n=1) is a degenerate case, a matrix with single element 2. This series involves products of binomial coefficients and is related to the superfactorial function.
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REFERENCES
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M. J. C. Gover, "The Explicit Inverse of Factorial Hankel Matrices", Department of Mathematics, University of Bradford, 1993
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LINKS
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IPJFACT, IPJFACT.
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FORMULA
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(n+1)! * Product[((i+1)! * (n-i)!); i=1, n-1]
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PROGRAM
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In MATLAB, the sequence is easily made by: for i=1:n det(gallery('ipjfact', i, 0)) end or, more explicitly, by: d = 1; for i=1:n-1 d = d*factorial(i+1)*factorial(n-i); end d = d*factorial(n+1);
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CROSSREFS
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Cf. A000178, A002514, A024356, A056886, A056887.
Sequence in context: A050643 A145513 A002860 this_sequence A052129 A141770 A060055
Adjacent sequences: A108075 A108076 A108077 this_sequence A108079 A108080 A108081
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KEYWORD
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easy,nonn
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AUTHOR
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Paul M. Payton (paul.payton(AT)lmco.com), Jun 03 2005
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