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 A384417 #9 May 30 2025 23:57:32
%S A384417 1,2592,1230336,294469632,49690312704,6822215811072,818458027622400,
%T A384417 89312567167549440,9086229152658358272,875874088323041460224,
%U A384417 80899222450192930308096,7217466034064795168145408,625687045828728598806134784,52946875811413468120885493760,4389120887020725640048536453120
%N A384417 Expansion of g.f. cosh(9*arctanh(8*sqrt(x))).
%F A384417 a(n) = 16^n*(105 + 400*n + 3392*n^2 + 512*n^3 + 4096*n^4)*(2*n)!/(105*(n!)^2).
%F A384417 O.g.f.: (1 + 2304*x + 516096*x^2 + 22020096*x^3 + 150994944*x^4)/(-64*x + 1)^(9/2).
%F A384417 E.g.f.: exp(32*x)*((105 + 512*x*(269 + 256*x*(73 + 512*x)))*BesselI(0, 32*x) + 512*x*(25 + 256*x*(65 + 512*x))*BesselI(1, 32*x))/105 + (131072*x*hypergeom([3/2, 2, 2], [1, 1, 1], 64*x))/105.
%p A384417 seq(coeff(series((1 + 2304*x + 516096*x^2 + 22020096*x^3 + 150994944*x^4)/(-64*x + 1)^(9/2), x, 15), x, k), k=0..14);
%t A384417 CoefficientList[Series[Cosh[9*ArcTanh[8*Sqrt[x]]],{x,0,14}],x] (* _Stefano Spezia_, May 29 2025 *)
%Y A384417 Cf. A383928, A384335, A285043, A285044, A285045, A285046.
%K A384417 nonn
%O A384417 0,2
%A A384417 _Karol A. Penson_, May 28 2025