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%I #10 Feb 19 2025 13:37:24
%S 1,9,1695,26215,120986775,9502702209,789204625209,34080236440965,
%T 1551341154742525575,141040042903795882275,52208336916743049297255,
%U 306352374268280009960745,1862930539686953773794528225,178800539000323387892726124675,34618577499107880715911257143875
%N a(n) = numerator( [x*y*z]^n 1/sqrt((1 - (x + y + z))*(1 - y - z^2)) ).
%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. 28.
%t a[n_]:=Numerator[SeriesCoefficient[1/Sqrt[(1-(x+y+z))(1-y-z^2)],{x,0,n},{y,0,n},{z,0,n}]]; Array[a,15,0]
%Y Cf. A381270 (denominator).
%Y Cf. A381271, A381272.
%K nonn,frac
%O 0,2
%A _Stefano Spezia_, Feb 18 2025