A207332 Double factorials (prime(n)-2)!!.

1, 1, 3, 15, 945, 10395, 2027025, 34459425, 13749310575, 213458046676875, 6190283353629375, 221643095476699771875, 319830986772877770815625, 13113070457687988603440625, 25373791335626257947657609375, 2980227913743310874726229193921875

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..16.

Formula

a(1) = 0!! := 1 and a(n) = Product_{k=0..(prime(n)-3)/2} (2*k+1), n >= 2.

a(n) = A006882(prime(n)-2). - Michel Marcus, Sep 12 2023

Example

For n = 5, prime(5) = A000040(5) = 11, 9!!= 1*3*5*7*9 = A040976(5)!! = A006882(9) = A001147(5) = 945.
a(5)^2 = 893025 == +1 (mod 11). - Wolfdieter Lang, May 07 2012

Mathematica

Table[(Prime[n] - 2)!!, {n, 1, 16}] (* Amiram Eldar, Sep 14 2023 *)

Prog

(PARI) a(n) = if (n==1, 1, prod(k=0, (prime(n)-3)/2, 2*k+1)); \\ Michel Marcus, Sep 12 2023

Crossrefs

Cf. A000040, A001147, A006882, A040976 (prime(n)-2).

Sequence in context: A077399 A219122 A293541 * A013409 A013408 A013412

Adjacent sequences: A207329 A207330 A207331 * A207333 A207334 A207335

Keyword

nonn

Author

Wolfdieter Lang, Feb 18 2012

Status

approved