A130332 Integer values of n!!/sum(i=0..n,n), with n>=1.

1, 1, 21, 1485, 6144, 225225, 17694720, 59520825, 6539968512, 24325703325, 145332633600, 14230536445125, 2596962041856000, 11288163762500625, 78354054748569600, 11665426077721040625, 86068915523813376000

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, May 24 2007

Keywords

• easy
• nonn

Comments

After the ninth term all the other numbers end in 0 or 5.

Examples

			5!! = 5*3*1 = 15; 5+4+3+2+1 = 15; 15/15 = 1.
13!! = 13*11*9*7*5*3*1 = 135135; 13+12+11+10+9+8+7+6+5+4+3+2+1 = 91; 135135/91 = 1485.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..466

Crossrefs

Cf. A130318, A126695, A108552.

Programs

Maple

P:=proc(n) local a,i,j,k,w; for i from 1 by 1 to n do k:=i; w:=i-2; while w>0 do k:=k*w; w:=w-2; od; j:=sum('w','w'=1..i); a:=k/j; if trunc(a)=a then print(a) fi; od; end: P(100);

Mathematica

Select[Table[n!!/((n(n+1))/2),{n,50}],IntegerQ] (* Harvey P. Dale, Jul 24 2019 *)