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%I #39 Sep 14 2023 15:38:05
%S 1,1,3,15,945,10395,2027025,34459425,13749310575,213458046676875,
%T 6190283353629375,221643095476699771875,319830986772877770815625,
%U 13113070457687988603440625,25373791335626257947657609375,2980227913743310874726229193921875
%N Double factorials (prime(n)-2)!!.
%C For the double factorials (2*n-1)!!, for n >= 1, see A001147, and n!! = A006882(n).
%C 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
%C a(n)^2 == A212159(n) (mod prime(n)), n >= 2. See also the W. Holsztyński link given there. - _Wolfdieter Lang_, May 07 2012
%F a(1) = 0!! := 1 and a(n) = Product_{k=0..(prime(n)-3)/2} (2*k+1), n >= 2.
%F a(n) = A006882(prime(n)-2). - _Michel Marcus_, Sep 12 2023
%e For n = 5, prime(5) = A000040(5) = 11, 9!!= 1*3*5*7*9 = A040976(5)!! = A006882(9) = A001147(5) = 945.
%e a(5)^2 = 893025 == +1 (mod 11). - _Wolfdieter Lang_, May 07 2012
%t Table[(Prime[n] - 2)!!, {n, 1, 16}] (* _Amiram Eldar_, Sep 14 2023 *)
%o (PARI) a(n) = if (n==1, 1, prod(k=0, (prime(n)-3)/2, 2*k+1)); \\ _Michel Marcus_, Sep 12 2023
%Y Cf. A000040, A001147, A006882, A040976 (prime(n)-2).
%K nonn
%O 1,3
%A _Wolfdieter Lang_, Feb 18 2012
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