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 A119883 #28 Jun 08 2023 10:57:55
%S A119883 1,2,0,-6,-1,50,14,-854,-323,24930,11804,-1111462,-631621,70271890,
%T A119883 46590634,-5980829430,-4531805575,659311412930,562021682744,
%U A119883 -91385427666758,-86555950096265,15555589905976050,16206870089730374,-3190048222084343446,-3625755168948973771
%N A119883 Expansion of E.g.f. (1 + 2*x + x^2/2) * sech(x).
%C A119883 Transform of binomial(2,n) under the matrix A119879.
%H A119883 G. C. Greubel, <a href="/A119883/b119883.txt">Table of n, a(n) for n = 0..480</a>
%F A119883 E.g.f.: (1 + 2*x + x^2/2) * sech(x).
%F A119883 a(n) = Sum_{k=0..n} A119879(n,k)*C(2,k).
%F A119883 a(n) = EulerE(n) + 2*n*EulerE(n-1) + n*(n-1)*EulerE(n-2)/2, n>1. - _Benedict W. J. Irwin_, May 30 2016
%t A119883 Table[If[n<2, n+1, EulerE[n] +2*n*EulerE[n-1] +n*(n-1)*EulerE[n-2]/2], {n,0,30}] (* _Benedict W. J. Irwin_, May 30 2016 *)
%t A119883 With[{nn=30},CoefficientList[Series[(1+2x+x^2/2)Sech[x],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Jul 01 2018 *)
%o A119883 (PARI) my(x='x+O('x^44)); Vec(serlaplace((1 + 2*x + x^2/2) / cosh(x))) \\ _Joerg Arndt_, Jun 01 2016
%o A119883 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( (1+2*x+x^2/2) /Cosh(x) ))); // _G. C. Greubel_, Jun 07 2023
%o A119883 (SageMath)
%o A119883 E=euler_number
%o A119883 def A119883(n):
%o A119883 if n<2: return n+1
%o A119883 else: return E(n) +2*n*E(n-1) +binomial(n,2)*E(n-2)
%o A119883 [A119883(n) for n in range(41)] # _G. C. Greubel_, Jun 07 2023
%Y A119883 Cf. A119879, A122045.
%K A119883 easy,sign
%O A119883 0,2
%A A119883 _Paul Barry_, May 26 2006