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 A081563 #14 Sep 08 2022 08:45:09
%S A081563 1,2,6,20,78,332,1566,7940,43518,253532,1573566,10295540,71069598,
%T A081563 513897932,3893187486,30741656420,252979075518,2161184079932,
%U A081563 19161309456126,175782239098580,1667967153565278,16331180476591532
%N A081563 Second binomial transform of expansion of exp(2*cosh(x)).
%C A081563 Binomial transform of A081562.
%H A081563 Vincenzo Librandi, <a href="/A081563/b081563.txt">Table of n, a(n) for n = 0..200</a>
%F A081563 E.g.f.: exp(2*x) * exp(2*cosh(x))/e^2 = exp(2*cosh(x)+2*x-2).
%p A081563 seq(coeff(series(exp(2*cosh(x)+2*x-2), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t A081563 With[{nn = 30}, CoefficientList[Series[Exp[2 Cosh[x] + 2 x - 2], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o A081563 (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(2*cosh(x)+2*x-2) )) \\ _G. C. Greubel_, Aug 13 2019
%o A081563 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*Cosh(x)+2*x-2) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2019
%o A081563 (Sage) [factorial(n)*( exp(2*cosh(x)+2*x-2) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 13 2019
%Y A081563 Cf. A000807, A081562.
%K A081563 easy,nonn
%O A081563 0,2
%A A081563 _Paul Barry_, Mar 22 2003