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

1,3

Comments

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

Links

Table of n, a(n) for n=1..23.

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A135989 A227772 A125652 * A364495 A340483 A018746

Adjacent sequences: A232698 A232699 A232700 * A232702 A232703 A232704

Keyword

nonn

Author

Alex Ratushnyak, Nov 28 2013

Status

approved