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 A381195 #13 May 29 2025 03:16:54
%S A381195 1,432,373248,403107840,487599243264,631928619270144,
%T A381195 857978513934778368,1204601833564428828672,1734626640332777513287680,
%U A381195 2547819609320783611516944384,3802273336964543978787469000704,5749037285490390495926653129064448,8788066841328079995004188536982208512
%N A381195 Expansion of g.f. (1 - sqrt(1 - 1728*x))/(864*x).
%H A381195 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. 23.
%F A381195 a(n) = (-27)^n*2^(1+6*n)*binomial(1/2,1+n).
%F A381195 E.g.f.: exp(864*x)*(BesselI(0, 864*x) - BesselI(1, 864*x)).
%F A381195 D-finite with recurrence (n+1)*a(n) +864*(-2*n+1)*a(n-1)=0. - _R. J. Mathar_, Feb 18 2025
%F A381195 a(n) ~ 1728^n / (sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, May 29 2025
%t A381195 CoefficientList[Series[(1-Sqrt[1-1728x])/(864x),{x,0,12}],x]
%Y A381195 Cf. A009971, A277757.
%K A381195 nonn
%O A381195 0,2
%A A381195 _Stefano Spezia_, Feb 16 2025