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

%I #24 Dec 10 2024 14:32:27

%S 0,0,1,2,7,3,9,69,177,60,2715,4500,42975,104580,91665,186795,3493665,

%T 13497435,97345395,442245825,2601636975,13003053525,70985324025,

%U 64585694250,57891366225,3576632909850,9411029102475,147580842959550,476966861546175,5708173568847750

%N a(n) = (n+1)!! mod n!!.

%C a(n) is divisible by A095987(n+1), and is nonzero for n > 1. - _Robert Israel_, Mar 10 2016

%H Robert Israel, <a href="/A227415/b227415.txt">Table of n, a(n) for n = 0..800</a>

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

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

%p seq(doublefactorial(n+1) mod doublefactorial(n), n=0..100); # _Robert Israel_, Mar 10 2016

%o (Python)

%o for n in range(2, 77):

%o prOdd = prEven = 1

%o for i in range(1, n, 2): prOdd *= i

%o for i in range(2, n, 2): prEven *= i

%o if n&1: print(prEven % prOdd, end=', ')

%o else: print(prOdd % prEven, end=', ')

%Y Cf. A006882, A095987.

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

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

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

%K nonn,easy

%O 0,4

%A _Alex Ratushnyak_, Jul 10 2013