A306184 a(n) = (2n+1)!! mod (2n)!! where k!! = A006882(k).

1, 7, 9, 177, 2715, 42975, 91665, 3493665, 97345395, 2601636975, 70985324025, 57891366225, 9411029102475, 476966861546175, 20499289200014625, 847876038362978625, 35160445175104123875, 1487419121780448231375, 945654757149212735625, 357657177058846280240625

Offset: 1

Author

Alex Ratushnyak, Jan 27 2019

Keywords

• nonn

Comments

a(n) is divisible by A049606(n). - Robert Israel, Jan 28 2019

Examples

			a(3) = A006882(7) mod A006882(6) = (7*5*3) mod (6*4*2) = 105 mod 48 = 9.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..403

Crossrefs

Cf. A006882, A049606, A122649, A129890, A232617, A232618, A306185.

Programs

Maple

f:= n -> doublefactorial(2*n+1) mod doublefactorial(2*n):
map(f, [$1..40]); # Robert Israel, Jan 28 2019

Mathematica

Mod[#[[2]],#[[1]]]&/@Partition[Range[2,42]!!,2] (* Harvey P. Dale, May 29 2025 *)

Python

o=e=1
for n in range(2, 99, 2):
  o*=n+1
  e*=n
  print(o%e, end=', ')

Formula

a(n) = A006882(2*n+1) mod A006882(2*n).