A276240 - OEIS

%I #19 Apr 06 2018 19:16:23

%S 1,25,225,38025,48841,439569,274730625,25672050625,25672050625,

%T 1405801492225,13983149754025,349578743850625,17129358448680625,

%U 166492622430255625,6659704897210225,24780761922519247225,2136708553523343255625,2136708553523343255625,11386519881725896209225625,892703158727310262803289

%N a(n) = denominator of rational fraction of function Gamma[5/4]^2 Gamma[n + 3/4]^2/(Gamma[3/4]^2 Gamma[n + 5/4]^2).

%C From _Robert Israel_, Sep 09 2016: (Start)

%C Square of denominator of pochhammer(3/4,n)/pochhammer(5/4,n) = Product_{odd k <= 4n+1} k^(k mod 4 - 2).

%C All terms are odd squares. (End)

%H Robert Israel, <a href="/A276240/b276240.txt">Table of n, a(n) for n = 0..734</a>

%p q:= 1: A[0]:= 1:

%p for i from 1 to 50 do

%p   p:= A[i-1]*(4*i+1);

%p   q:= q*(4*i-1);

%p   g:= igcd(p,q);

%p   A[i]:= p/g;

%p   q:= q/g;

%p od:

%p seq(A[i]^2,i=0..50); # _Robert Israel_, Sep 09 2016

%t Table[Denominator[Pochhammer[3/4, n]^2/Pochhammer[5/4, n]^2], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 06 2018 *)

%Y Cf. A276239 (numerators).

%K nonn,frac

%O 0,2

%A _Artur Jasinski_, Aug 25 2016