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 A081561 #14 Sep 08 2022 08:45:09
%S A081561 1,2,8,32,176,992,6848,48512,398336,3356672,31751168,307914752,
%T A081561 3282292736,35827392512,423577223168,5121571684352,66347485822976,
%U A081561 877984005619712,12344359378485248,177098976447168512
%N A081561 Second binomial transform of expansion of exp(cosh(2*x)).
%C A081561 Binomial transform of A081560.
%H A081561 Vincenzo Librandi, <a href="/A081561/b081561.txt">Table of n, a(n) for n = 0..200</a>
%F A081561 E.g.f.: exp(2*x) * exp(cosh(2*x))/e = exp(cosh(2*x)+2*x-1)
%p A081561 seq(coeff(series(exp(cosh(2*x)+2*x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t A081561 With[{nn = 30}, CoefficientList[Series[Exp[Cosh[2 x] + 2 x - 1], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o A081561 (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(2*x)+2*x-1) )) \\ _G. C. Greubel_, Aug 13 2019
%o A081561 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(2*x)+2*x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2019
%o A081561 (Sage) [factorial(n)*( exp(cosh(2*x)+2*x-1) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 13 2019
%Y A081561 Cf. A081559, A081560.
%K A081561 easy,nonn
%O A081561 0,2
%A A081561 _Paul Barry_, Mar 22 2003