A232701 a(n) = (2*n-1)!! mod n!, where double factorial is A006882.

0, 1, 3, 9, 105, 315, 4095, 11025, 348705, 1545075, 17931375, 93087225, 3764185425, 45589819275, 1060569885375, 15877899662625, 900941666625, 5722531807867875, 90088576482279375, 1688777976676415625, 18148954872023600625, 320586579951629866875, 11054393914490520969375

Offset: 1

Author

Alex Ratushnyak, Nov 28 2013

Keywords

• nonn

Comments

(2n-1)!! is the product of first n odd numbers.

Examples

			a(4) = 1*3*5*7 mod (1*2*3*4) = 105 mod 24 = 9.
		

Crossrefs

Cf. A006882, A232618, A024502 (floor((2*n-1)!! / n!)).

Programs

Mathematica

o = 1; Reap[For[n = 1, n <= 99, n += 2, o *= n; m = Mod[o, (Quotient[n, 2] + 1)!]; Sow[m]]][[2, 1]] (* Jean-François Alcover, Oct 05 2017, translated from Alex Ratushnyak's Python code *)

Python

import math
o=1
for n in range(1,99,2):
  o*=n
  print(o % math.factorial(n//2+1), end=', ')