A306184 - OEIS

%I #20 Jan 29 2019 04:36:31

%S 1,7,9,177,2715,42975,91665,3493665,97345395,2601636975,70985324025,

%T 57891366225,9411029102475,476966861546175,20499289200014625,

%U 847876038362978625,35160445175104123875,1487419121780448231375,945654757149212735625,357657177058846280240625

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

%C a(n) is divisible by A049606(n). - _Robert Israel_, Jan 28 2019

%H Robert Israel, <a href="/A306184/b306184.txt">Table of n, a(n) for n = 1..403</a>

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

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

%p f:= n -> doublefactorial(2*n+1) mod doublefactorial(2*n):

%p map(f, [$1..40]); # _Robert Israel_, Jan 28 2019

%o (Python)

%o o=e=1

%o for n in range(2, 99, 2):

%o   o*=n+1

%o   e*=n

%o   print str(o%e)+',',

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

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Jan 27 2019