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A232617 Product of first n odd numbers plus product of first n even numbers: (2n-1)!! + (2n)!!, where k!! = A006882(k).

%I A232617 #16 May 05 2021 19:22:04
%S A232617 3,11,63,489,4785,56475,780255,12348945,220253985,4370620275,
%T A232617 95498916975,2278224696825,58917607974225,1641787169697675,
%U A232617 49040157044253375,1563094742062478625,52953322446161762625,1899986948191060603875,71977860935783603175375,2870913642898706235455625
%N A232617 Product of first n odd numbers plus product of first n even numbers: (2n-1)!! + (2n)!!, where k!! = A006882(k).
%F A232617 a(n) = A006882(2*n-1) + A006882(2*n).
%F A232617 a(n) = A001147(n) + A000165(n).
%F A232617 a(n) +(-4*n+3)*a(n-1) +2*(n-1)*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Nov 23 2014
%e A232617 a(3) = 1*3*5 + 2*4*6 = 15 + 48 = 63.
%t A232617 Table[n!!+(n+1)!!,{n,1,41,2}] (* _Harvey P. Dale_, Jan 22 2019 *)
%o A232617 (Python)
%o A232617 o=e=1
%o A232617 for n in range(1,99,2):
%o A232617   o*=n
%o A232617   e*=n+1
%o A232617   print(str(e+o), end=',')
%o A232617 (PARI) a(n)=prod(i=1,n,2*i-1)+prod(i=1,n,2*i) \\ _Ralf Stephan_, Nov 28 2013
%Y A232617 Cf. A006882, A122649, A129890.
%K A232617 nonn
%O A232617 1,1
%A A232617 _Alex Ratushnyak_, Nov 27 2013