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A010791
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a(n) = n!*(n+2)!/2.
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18
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1, 3, 24, 360, 8640, 302400, 14515200, 914457600, 73156608000, 7242504192000, 869100503040000, 124281371934720000, 20879270485032960000, 4071457744581427200000, 912006534786239692800000, 232561666370491121664000000, 66977759914701443039232000000
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OFFSET
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0,2
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COMMENTS
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Also determinant of n X n matrix with m(i,j) = i^2 if i=j, otherwise 1. - Robert G. Wilson v, Jan 28 2002
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, Oct 21 2008
Equals (-1)^n * (1, 1, 3, 24, 360, ...) dot (1, -4, 9, -16, 25, ...). E.g., a(4) = (1, 1, 3, 24, 360) dot (1, -4, 9, -16, 25) = 1 - 4 + 27 - 384 + 9000 = 8640. - Gary W. Adamson, Apr 21 2009
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = 2*BesselI(2,2) = 2*A229020.
Sum_{n>=0} (-1)^n/a(n) = 2*BesselJ(2,2). (End)
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MAPLE
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f := n->n!*(n+2)!/2;
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MATHEMATICA
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PROG
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(Magma) [Factorial(n)* Factorial(n+2) / 2: n in [0..20]]; // Vincenzo Librandi, Jun 11 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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