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

3, 11, 63, 489, 4785, 56475, 780255, 12348945, 220253985, 4370620275, 95498916975, 2278224696825, 58917607974225, 1641787169697675, 49040157044253375, 1563094742062478625, 52953322446161762625, 1899986948191060603875, 71977860935783603175375, 2870913642898706235455625

Offset: 1

Author

Alex Ratushnyak, Nov 27 2013

Keywords

• nonn

Examples

			a(3) = 1*3*5 + 2*4*6 = 15 + 48 = 63.
		

Crossrefs

Cf. A006882, A122649, A129890.

Programs

Mathematica

Table[n!!+(n+1)!!,{n,1,41,2}] (* Harvey P. Dale, Jan 22 2019 *)

PARI

a(n)=prod(i=1,n,2*i-1)+prod(i=1,n,2*i) \\ Ralf Stephan, Nov 28 2013

Python

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

Formula

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

a(n) = A001147(n) + A000165(n).

a(n) +(-4*n+3)*a(n-1) +2*(n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 23 2014