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A059332
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Determinant of n X n matrix A defined by A[i,j] = (i+j-1)! for 1 <= i,j <= n.
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7
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1, 2, 24, 3456, 9953280, 859963392000, 3120635156889600000, 634153008009974906880000000, 9278496603801318870491332608000000000, 12218100099725239100847669366019325952000000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Hankel transform of n! (A000142(n)) and of A003319. [From Paul Barry (pbarry(AT)wit.ie), Oct 07 2008]
Hankel transform of A000255. [From Paul Barry (pbarry(AT)wit.ie), Apr 22 2009]
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FORMULA
| a(n) = a(n-1)*(n!)*(n-1)! for n >= 2 so a(n) = product k=1, 2, ..., n k!*(k-1)!
a(n)=2^C(n,2)*product{k=1..(n-1), C(k+2,2)^(n-1-k)}. [From Paul Barry (pbarry(AT)wit.ie), Jan 15 2009]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009: (Start)
a(n) = n!*product(k!, k=0..n-1)^2
(End)
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EXAMPLE
| a(4) = 3456 because the relevant matrix is {1 2 6 24 / 2 6 24 120 / 6 24 120 720 / 24 120 720 5040 } and the determinant is 3456.
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MAPLE
| with(linalg): Digits := 500: A059332 := proc(n) local A, i, j: A := array(1..n, 1..n): for i from 1 to n do for j from 1 to n do A[i, j] := (i+j-1)! od: od: RETURN(det(A)) end: for n from 1 to 20 do printf(`%d, `, A059332(n)) od;
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CROSSREFS
| Cf. A010790.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009: (Start)
Cf. A162014 and A055209.
(End)
Sequence in context: A111428 A111429 A111430 * A000794 A159907 A088912
Adjacent sequences: A059329 A059330 A059331 * A059333 A059334 A059335
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KEYWORD
| nonn,easy
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AUTHOR
| Noam Katz (noamkj(AT)hotmail.com), Jan 26 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 29 2001
Offset corrected. Comment and formula aligned with new offset by Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 24 2009
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