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 A130318 Integer values of n!!/S(n), where S(n) is the sum of all odd numbers minor or equal to n, if n is odd, or the sum of all even numbers minor or equal to n, if n is even. 3

%I

%S 1,1,4,128,11520,143360,425425,2064384,619315200,280284364800,

%T 6801567252480,27512370460575,178541140377600,152355106455552000,

%U 167834385271436083200,6074006324109115392000,29734853645550994565625

%N Integer values of n!!/S(n), where S(n) is the sum of all odd numbers minor or equal to n, if n is odd, or the sum of all even numbers minor or equal to n, if n is even.

%C After the eighth term all the numbers end with 0 or 5.

%H Jayanta Basu, <a href="/A130318/b130318.txt">Table of n, a(n) for n = 0..100</a>

%F Integer of the form n!!/A005408, for n odd and n!!/A002378 (offset 2) for n even.

%e 6 --> 6!! = 48; 6 + 4 + 2 = 12; 48/12 = 4.

%e 17 --> 17!! = 34459425; 17 + 15 + 13 + 11 + 9 + 7 + 5 + 3 + 1 = 81; 34459425/81 = 425425.

%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:=i; w:=i-2; while w>0 do j:=j+w; w:=w-2; od; a:=k/j; if trunc(a)=a then print(a) fi; od; end: P(100);

%t Select[Table[Times @@ (t = If[OddQ[n], Range[1, n, 2], Range[2, n, 2]])/Plus @@ t, {n, 41}], IntegerQ] (* _Jayanta Basu_, Aug 12 2013 *)

%Y Cf. A108552, A000290, A005408, A130319.

%K easy,nonn

%O 0,3

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 23 2007

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Last modified May 6 12:44 EDT 2021. Contains 343585 sequences. (Running on oeis4.)