A381186 a(n) = denominator( [x^n] hypergeom([1/4, 3/4], [1], 2^6*x/3^2)/sqrt(1 - 4*x) ).

1, 3, 27, 243, 729, 6561, 177147, 177147, 531441, 129140163, 387420489, 3486784401, 31381059609, 94143178827, 847288609443, 22876792454961, 7625597484987, 205891132094649, 50031545098999707, 150094635296999121, 1350851717672992089, 1350851717672992089, 4052555153018976267

Offset

0,2

Links

Table of n, a(n) for n=0..22.

S. Hassani, J.-M. Maillard, and N. Zenine, On the diagonals of rational functions: the minimal number of variables (unabridged version), arXiv:2502.05543 [math-ph], 2025. See p. 21.

Mathematica

a[n_]:=Denominator[SeriesCoefficient[Hypergeometric2F1[1/4, 3/4, 1, 2^6x/3^2]/Sqrt[1-4x], {x, 0, n}]]; Array[a, 23, 0]

Crossrefs

Cf. A381185 (numerators).

Sequence in context: A065100 A035088 A344724 * A268094 A013708 A102518

Adjacent sequences: A381183 A381184 A381185 * A381187 A381188 A381189

Keyword

nonn,frac

Author

Stefano Spezia, Feb 16 2025

Status

approved