A381185 a(n) = numerator( [x^n] hypergeom([1/4, 3/4], [1], 2^6*x/3^2)/sqrt(1 - 4*x) ).

1, 10, 374, 15484, 230210, 10919020, 1635492740, 9461595400, 169793701330, 253354748427220, 4762913165558548, 272892459138645320, 15830057357705343116, 309116222832740182552, 18252959497023816606200, 3254657058859020013332688, 7203918574814465440160390, 1297593844520826560448239324

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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_]:=Numerator[SeriesCoefficient[Hypergeometric2F1[1/4, 3/4, 1, 2^6x/3^2]/Sqrt[1-4x], {x, 0, n}]]; Array[a, 18, 0]

Prog

(PARI) my(x='x+O('x^30)); Vec(apply(numerator, hypergeom([1/4, 3/4], [1], 2^6*x/3^2)/sqrt(1 - 4*x))) \\ Michel Marcus, Feb 16 2025

Crossrefs

Cf. A381186 (denominators).

Sequence in context: A392322 A291530 A358801 * A117312 A200804 A277663

Adjacent sequences: A381182 A381183 A381184 * A381186 A381187 A381188

Keyword

nonn,frac

Author

Stefano Spezia, Feb 16 2025

Status

approved