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A179442
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a(n) = ((n-1)! * (n+1)!) / n.
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1
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2, 3, 16, 180, 3456, 100800, 4147200, 228614400, 16257024000, 1448500838400, 158018273280000, 20713561989120000, 3212195459235840000, 581636820654489600000, 121600871304831959040000
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = Product_{k=1..n} (k * A020725(k)) / (n^2) = Product_{k=1..n} (k * (k+1)) / (n^2).
G.f.: 1 + G(0), where G(k)= 1 + x*(k+1)/(1 - (k+2)/(k+2 + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 08 2013
Sum_{n>=1} (-1)^(n+1)/a(n) = BesselJ(2,2) - BesselJ(3,2). (End)
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EXAMPLE
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a(5) = ((5-1)! * (5+1)!) / 5 = (4! * 6!) / 5 = (24 * 720) / 5 = 17280 / 5 = 3456.
a(5) = ((5 -1)!^2) * (5+1) = 24^2 * 6 = 3456.
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MATHEMATICA
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Table[(n - 1)!*(n + 1)!/n, {n, 1, 15}] (* Amiram Eldar, Jan 18 2021 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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