A227415 a(n) = (n+1)!! mod n!!.

0, 0, 1, 2, 7, 3, 9, 69, 177, 60, 2715, 4500, 42975, 104580, 91665, 186795, 3493665, 13497435, 97345395, 442245825, 2601636975, 13003053525, 70985324025, 64585694250, 57891366225, 3576632909850, 9411029102475, 147580842959550, 476966861546175, 5708173568847750

Offset: 0

Author

Alex Ratushnyak, Jul 10 2013

Keywords

• nonn
• easy

Comments

a(n) is divisible by A095987(n+1), and is nonzero for n > 1. - Robert Israel, Mar 10 2016

Examples

			a(4) = 5*3 mod 4*2 = 15 mod 8 = 7.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..800

Crossrefs

Cf. A006882, A095987.

Cf. A007911: (n-1)!! - (n-2)!!

Cf. A007912: (n-1)!! - (n-2)!! (mod n).

Cf. A060696: (n-1)!! + (n-2)!! except first two terms.

Programs

Maple

seq(doublefactorial(n+1) mod doublefactorial(n), n=0..100); # Robert Israel, Mar 10 2016

Python

for n in range(2, 77):
    prOdd = prEven = 1
    for i in range(1, n, 2): prOdd *= i
    for i in range(2, n, 2): prEven *= i
    if n&1: print(prEven % prOdd, end=', ')
    else:   print(prOdd % prEven, end=', ')

Formula

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