login
A276239
a(n) = numerator of rational fraction of function (Gamma[5/4]^2 Gamma[n + 3/4]^2)/(Gamma[3/4]^2 Gamma[n + 5/4]^2).
2
1, 9, 49, 5929, 5929, 43681, 23107249, 1871687169, 1651690881, 80932853169, 728395678521, 16627205056609, 749581550409169, 6746233953682521, 251244785594209, 874583098653441529, 70841230990928763849, 66794010904910569401, 336708608971654180350441, 25044441989627170439289, 1929658795768681119896329
OFFSET
0,2
COMMENTS
From Robert Israel, Sep 09 2016: (Start)
Square of numerator of pochhammer(3/4,n)/pochhammer(5/4,n) = Product_{odd k <= 4n+1} k^(k mod 4 - 2).
All terms are odd squares. (End)
LINKS
MAPLE
q:= 1: A[0]:= 1:
for i from 1 to 50 do
p:= A[i-1]*(4*i-1);
q:= q*(4*i+1);
g:= igcd(p, q);
A[i]:= p/g;
q:= q/g;
od:
seq(A[i]^2, i=0..50); # Robert Israel, Sep 09 2016
MATHEMATICA
Table[Numerator[Pochhammer[3/4, n]^2/Pochhammer[5/4, n]^2], {n, 0, 20}] (* Vaclav Kotesovec, Apr 06 2018 *)
CROSSREFS
Cf. A276240 (denominators).
Sequence in context: A050638 A088064 A080812 * A116169 A280549 A084367
KEYWORD
nonn,frac
AUTHOR
Artur Jasinski, Aug 25 2016
STATUS
approved