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%I #9 Feb 20 2025 08:37:44
%S 1,6,2835,144375,9656521875,727613515629,1924950961452519,
%T 169849119537100575,515343459815505282121875,
%U 49523686986654845229890625,156852007784587147805477109405,15901454576103641443903862431665,1683931647757461343713885153275036775,177089976268148398718338641838887890625
%N a(n) = numerator( [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) = numerator( 4*(4*n - 1)!*Gamma(n+1/2)^2/(Pi*(n-1)!*(n!)^5) ) with a(0) = 1.
%t a[0]=1; a[n_]:=Numerator[4*(4*n - 1)!*Gamma[n+1/2]^2/(Pi*(n-1)!n!^5)]; Array[a,14,0]
%Y Cf. A381298 (denominator).
%K nonn,frac
%O 0,2
%A _Stefano Spezia_, Feb 19 2025