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A207332
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Double factorials (prime(n)-2)!!.
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2
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1, 1, 3, 15, 945, 10395, 2027025, 34459425, 13749310575, 213458046676875, 6190283353629375, 221643095476699771875, 319830986772877770815625, 13113070457687988603440625, 25373791335626257947657609375, 2980227913743310874726229193921875
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OFFSET
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1,3
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COMMENTS
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For the double factorials (2*n-1)!!, for n >= 1, see A001147, and n!! = A006882(n).
For a(n) Modd prime(n) see a comment on A209389 stating the analog of Wilson's theorem for Modd prime(n). For Modd n, (not to be confused with mod n) see a comment on A203571. - Wolfdieter Lang, Mar 28 2012
a(n)^2 == A212159(n) (mod prime(n)), n >= 2. See also the W. Holsztyński link given there. - Wolfdieter Lang, May 07 2012
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LINKS
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FORMULA
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a(1) = 0!! := 1 and a(n) = Product_{k=0..(prime(n)-3)/2} (2*k+1), n >= 2.
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EXAMPLE
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MATHEMATICA
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Table[(Prime[n] - 2)!!, {n, 1, 16}] (* Amiram Eldar, Sep 14 2023 *)
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PROG
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(PARI) a(n) = if (n==1, 1, prod(k=0, (prime(n)-3)/2, 2*k+1)); \\ Michel Marcus, Sep 12 2023
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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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