This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381267 #10 Feb 19 2025 13:37:44
%S A381267 1,15,31185,6381375,409933148625,115551955934415,561860686475913825,
%T A381267 179982394552964750175,245527483089290688069980625,
%U A381267 84259935283701238220954169375,473788223464393905637179153328785,169752647693877043154936308907932575,15821279983229628402902553309640505635425
%N A381267 a(n) = numerator( [(x*y*z*u)^n] 1/sqrt(1 - (x + y + z + u*(y + z))) ).
%H A381267 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. 24.
%F A381267 a(n) = numerator( [x^n] hypergeom( [1/2, 1/6, 1/2, 5/6], [1, 1, 1], 108*x) ).
%F A381267 a(n) = numerator( 2^(2*n-1) * 27^n * Gamma(n+1/6) * Gamma(n+1/2)^2 * Gamma(n+5/6)/(Pi^2 * (n!)^4) ).
%t A381267 a[n_]:=Numerator[SeriesCoefficient[1/Sqrt[1-(x+y+z+u(y+z))],{x,0,n},{y,0,n},{z,0,n},{u,0,n}]]; Array[a,13,0]
%Y A381267 Cf. A381268 (denominator).
%Y A381267 Cf. A009971, A134375.
%K A381267 nonn,frac
%O A381267 0,2
%A A381267 _Stefano Spezia_, Feb 18 2025