A381298 - OEIS

%I #7 Feb 20 2025 08:37:48

%S 1,1,8,4,2048,1024,16384,8192,134217728,67108864,1073741824,536870912,

%T 274877906944,137438953472,2199023255552,1099511627776,

%U 576460752303423488,288230376151711744,4611686018427387904,2305843009213693952,1180591620717411303424,590295810358705651712,9444732965739290427392

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

%H S. Hassani, J.-M. Maillard, and N. Zenine, <a href="https://arxiv.org/abs/2502.05543">On the diagonals of rational functions: the minimal number of variables (unabridged version)</a>, arXiv:2502.05543 [math-ph], 2025. See p. 46.

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

%t 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]

%Y Cf. A381297 (numerator).

%K nonn,frac

%O 0,3

%A _Stefano Spezia_, Feb 19 2025