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1, 3, 24, 360, 8640, 302400, 14515200, 914457600, 73156608000, 7242504192000, 869100503040000, 124281371934720000, 20879270485032960000, 4071457744581427200000, 912006534786239692800000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also determinant of n X n matrix with m(i,j) = i^2 if i=j otherwise 1. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 28 2002
Partial products of positive values of A005563. - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2008
This sequence has been shown to contain infinitely many squares. From the Hong and Liu abstract: Recently Cilleruelo proved that the product Product[k=1..n](k^2 + 1) is a square only for n = 3 which confirms a conjecture of Amdeberhan, Medina and Moll. In this paper, we show that the sequence Product[k=2..n](k^2 - 1)} contains infinitely many squares. Furthermore, we determine all squares in this sequence. We also give a formula for the p-adic valuation of the terms in this sequence. - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2008
Equals (-1)^n * (1, 1, 3, 24, 360,...) dot (1, -4, 9, -16, 25,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 21 2009]
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REFERENCES
| J. Cilleruelo, Squares in (1^2 + 1) . . . (n^2 + 1), J. Number Theory 128 (2008), 2488-2491.
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LINKS
| Shaofang Hong, Xingjiang Liu, Squares in (2^2-1)...(n^2-1) and p-adic valuation, Oct 19, 2008.
Index entries for sequences related to factorial numbers
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EXAMPLE
| Example: a(4) = 8640 = (1, 1, 3, 24, 360) dot (1, -4, 9, -16, 25) = (1, -4, 27, -384, 9000). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 21 2009]
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MAPLE
| f := n->n!*(n+2)!/2;
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MATHEMATICA
| Table[n!(n+2)!/2, {n, 0, 20}] (*From Vladimir Joseph Stephan Orlovsky, Apr 03 2011*)
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PROG
| (Other) sage: [stirling_number1(n, 1)*factorial(n-3)/2 for n in xrange(3, 18)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]
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CROSSREFS
| Sequence in context: A082166 A144003 A153389 * A145169 A193210 A065761
Adjacent sequences: A010788 A010789 A010790 * A010792 A010793 A010794
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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