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A108078
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Determinant of a Hankel matrix with factorial elements.
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1
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2, 12, 576, 414720, 7166361600, 4334215495653800, 125824009529730280000000, 230121443464257970000000000000000, 33669808618214310000000000000000000000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
| M. J. C. Gover, "The Explicit Inverse of Factorial Hankel Matrices", Department of Mathematics, University of Bradford, 1993
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LINKS
| IPJFACT, IPJFACT.
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FORMULA
| (n+1)! * Product[((i+1)! * (n-i)!); i=1, n-1]
a(n)=A059332(n)*(n+1)!
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MATHEMATICA
| A108078[n_]:=Det[Table[(i+j)!, {i, 1, n}, {j, 1, n}]]; Array[A108078, 20] (* Enrique Perez Herrero, May 20 2011 *)
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PROG
| 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
| Cf. A000178, A002514, A024356, A056886, A056887.
Sequence in context: A050643 A145513 A002860 * A052129 A173104 A141770
Adjacent sequences: A108075 A108076 A108077 * A108079 A108080 A108081
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KEYWORD
| easy,nonn
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AUTHOR
| Paul M. Payton (paul.payton(AT)lmco.com), Jun 03 2005
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