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%I #9 Jul 05 2021 02:42:35
%S 1,2,2243,1954,8798,32865944,131921,762433904,4641465428984,
%T 212594615488,1302317393264,7413941047079296,25240278679125376,
%U 4579921610967660032,12897123674403614072,8798331231517965002752,1689908720214734836736,1765127996286967623157194752
%N Numerator of a certain Selberg integral.
%D Donald St. P. Richards, Analogs and extensions of Selberg's integrals, pp. 108-137 of D. Stanton, Ed., "q-Series and Partitions", Springer, 1989, see esp. p. 125.
%e 1/12, 2/75, 2243/147000, 1954/165375, 8798/800415, ...
%t a[n_] := Numerator[2^n*3/((n + 1)^2*(2*n + 1)*(4*n + 3)) * HypergeometricPFQ[{-n, 1, 1}, {n + 2, 1/2 - n}, 1/4]]; Array[a, 20] (* _Amiram Eldar_, Jul 05 2021 *)
%Y Cf. A051104 (denominators).
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Amiram Eldar_, Jul 05 2021