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).

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

Robert Israel, Table of n, a(n) for n = 0..734

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

Adjacent sequences: A276236 A276237 A276238 * A276240 A276241 A276242

Keyword

nonn,frac

Author

Artur Jasinski, Aug 25 2016

Status

approved