A126868 a(n) = (n+1)!! mod n.

0, 1, 2, 3, 3, 3, 6, 1, 6, 5, 1, 3, 8, 7, 0, 1, 13, 9, 1, 15, 0, 11, 1, 9, 0, 13, 0, 7, 17, 15, 1, 1, 0, 17, 0, 27, 6, 19, 0, 25, 9, 21, 1, 11, 0, 23, 46, 33, 0, 25, 0, 39, 30, 27, 0, 49, 0, 29, 58, 15, 50, 31, 0, 1, 0, 33, 1, 51, 0, 35, 1, 9, 27, 37, 0, 19, 0, 39, 78, 65, 0, 41, 82, 63, 0, 43

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 16 2007

Keywords

• easy
• nonn

Examples

			n=3 (n+1)!! = 4!! = 8; (8 mod 3) = 2.
n=4 (n+1)!! = 5!! = 15; (15 mod 4) = 3.
		

Links

• James C. McMahon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006882, A000165, A001147, A119688.

Programs

Maple

P:=proc(n) local i,j,k,w; for i from 1 by 1 to n do k:=i+1; w:=i-1; while w>0 do k:=k*w; w:=w-2; od; j:=(k mod i); print(j); od; end: P(100);

Mathematica

Table[Mod[(n+1)!!,n],{n,86}] (* James C. McMahon, Dec 27 2024 *)

PARI

df(n) = prod(i=0, (n-1)\2, n - 2*i );
a(n) = df(n+1) % n; \\ Michel Marcus, Aug 22 2016