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%I #7 Jul 24 2019 15:16:43
%S 1,1,21,1485,6144,225225,17694720,59520825,6539968512,24325703325,
%T 145332633600,14230536445125,2596962041856000,11288163762500625,
%U 78354054748569600,11665426077721040625,86068915523813376000
%N Integer values of n!!/sum(i=0..n,n), with n>=1.
%C After the ninth term all the other numbers end in 0 or 5.
%H Harvey P. Dale, <a href="/A130332/b130332.txt">Table of n, a(n) for n = 0..466</a>
%e 5!! = 5*3*1 = 15; 5+4+3+2+1 = 15; 15/15 = 1.
%e 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.
%p 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);
%t Select[Table[n!!/((n(n+1))/2),{n,50}],IntegerQ] (* _Harvey P. Dale_, Jul 24 2019 *)
%Y Cf. A130318, A126695, A108552.
%K easy,nonn
%O 0,3
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 24 2007