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 A081558 #29 Apr 24 2023 06:48:51
%S A081558 1,2,5,14,44,152,575,2354,10379,48902,245240,1301984,7294589,42959282,
%T A081558 265263185,1712168654,11528506124,80783015192,588097479635,
%U A081558 4439382164114,34699233959759,280381494540182,2339287666524440,20125268756209664,178348602246900569
%N A081558 Exponential generating function: exp(cosh(x)+2*x-1).
%C A081558 Old definition was "Second binomial transform of expansion of exp(cosh(x))".
%C A081558 Binomial transform of A081557.
%H A081558 Vincenzo Librandi, <a href="/A081558/b081558.txt">Table of n, a(n) for n = 0..200</a>
%F A081558 E.g.f.: exp(2*x) * exp(cosh(x))/e.
%p A081558 seq(coeff(series(exp(cosh(x)+2*x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t A081558 With[{nn = 30}, CoefficientList[Series[Exp[Cosh[x] + 2 x - 1], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o A081558 (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(x)+2*x-1) )) \\ _G. C. Greubel_, Aug 13 2019
%o A081558 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(x)+2*x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2019
%o A081558 (Sage) [factorial(n)*( exp(cosh(x)+2*x-1) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 13 2019
%Y A081558 Cf. A005046, A081557.
%K A081558 easy,nonn
%O A081558 0,2
%A A081558 _Paul Barry_, Mar 22 2003
%E A081558 Definition edited by _N. J. A. Sloane_, Dec 12 2021