A051103 Numerator of a certain Selberg integral.

1, 2, 2243, 1954, 8798, 32865944, 131921, 762433904, 4641465428984, 212594615488, 1302317393264, 7413941047079296, 25240278679125376, 4579921610967660032, 12897123674403614072, 8798331231517965002752, 1689908720214734836736, 1765127996286967623157194752

Offset

1,2

References

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.

Links

Table of n, a(n) for n=1..18.

Example

1/12, 2/75, 2243/147000, 1954/165375, 8798/800415, ...

Mathematica

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 *)

Crossrefs

Cf. A051104 (denominators).

Sequence in context: A365179 A028487 A073476 * A005800 A200170 A280899

Adjacent sequences: A051100 A051101 A051102 * A051104 A051105 A051106

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Amiram Eldar, Jul 05 2021

Status

approved