A381298 a(n) = denominator( [x^n] hypergeom([1/2, 1/2, 1/2, 1/4, 3/4], [1, 1, 1, 1], 256*x) ).

1, 1, 8, 4, 2048, 1024, 16384, 8192, 134217728, 67108864, 1073741824, 536870912, 274877906944, 137438953472, 2199023255552, 1099511627776, 576460752303423488, 288230376151711744, 4611686018427387904, 2305843009213693952, 1180591620717411303424, 590295810358705651712, 9444732965739290427392

Offset

0,3

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. 46.

Formula

a(n) = denominator( 4*(4*n - 1)!*Gamma(n+1/2)^2/(Pi*(n-1)!*(n!)^5) ) with a(0) = 1.

Mathematica

a[n_]:=Denominator[SeriesCoefficient[HypergeometricPFQ[{1/2, 1/2, 1/2, 1/4, 3/4}, {1, 1, 1, 1}, 256*x], {x, 0, n}]]; Array[a, 23, 0]

Crossrefs

Cf. A381297 (numerator).

Sequence in context: A231234 A096687 A326955 * A199374 A289538 A154224

Adjacent sequences: A381295 A381296 A381297 * A381299 A381300 A381301

Keyword

nonn,frac

Author

Stefano Spezia, Feb 19 2025

Status

approved