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 A081439 #12 Sep 08 2022 08:45:09
%S A081439 1,2,5,14,53,242,1505,10334,89129,797090,8618045,94186094,1220350301,
%T A081439 15745031954,237660317081,3534411032894,60889488170321,
%U A081439 1025300949710402,19847126167227509,373194859437512654,8017708459752349061
%N A081439 Expansion of exp(2*x)*cosh(x/sqrt(1 - x^2)).
%C A081439 Second binomial transform of expansion of cosh(x/sqrt(1-x^2)).
%H A081439 G. C. Greubel, <a href="/A081439/b081439.txt">Table of n, a(n) for n = 0..445</a>
%F A081439 D-finite with recurrence: a(n) = 4*a(n-1) + 3*(n-3)*(n-1)*a(n-2) - 6*(n-2)*(2*n-5)*a(n-3) - 3*(n-3)*(n-2)*(n^2 - 7*n + 8)*a(n-4) + 12*(n-4)^2*(n-3)*(n-2)*a(n-5) + (n-5)*(n-4)*(n-3)*(n-2)*(n^2 - 10*n + 12)*a(n-6) - 2*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(2*n-11)*a(n-7) + 4*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*a(n-8). - _Vaclav Kotesovec_, Oct 29 2014
%p A081439 seq(coeff(series(exp(2*x)*cosh(x/sqrt(1-x^2)), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 14 2019
%t A081439 With[{nn=20}, CoefficientList[Series[Exp[2*x]*Cosh[x/Sqrt[1-x^2]], {x, 0, nn}], x] * Range[0, nn]!] (* _Vaclav Kotesovec_, Oct 29 2014 *)
%o A081439 (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(2*x)*cosh(x/sqrt(1-x^2)) )) \\ _G. C. Greubel_, Aug 14 2019
%o A081439 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*x)*Cosh(x/Sqrt(1-x^2)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 14 2019
%o A081439 (Sage) [factorial(n)*( exp(2*x)*cosh(x/sqrt(1-x^2)) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 14 2019
%Y A081439 Cf. A081440.
%K A081439 easy,nonn
%O A081439 0,2
%A A081439 _Paul Barry_, Mar 21 2003