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 A084098 #19 Oct 14 2022 08:55:10
%S A084098 0,1,2,11,36,341,1702,23071,154056,2691241,22470602,479886131,
%T A084098 4808343276,121361260541,1418683841902,41316096677191,551971861815696,
%U A084098 18218322689532241,273815850521907602,10100775754144668251
%N A084098 Expansion of e.g.f. exp(x)*tan(2*x)/2.
%C A084098 Binomial transform of expansion of tan(2x)/2 (0,1,0,8,0,256,...).
%H A084098 Robert Israel, <a href="/A084098/b084098.txt">Table of n, a(n) for n = 0..430</a>
%F A084098 E.g.f.: exp(x)*tan(2*x)/2.
%F A084098 a(n) ~ n! * (exp(Pi/4)-(-1)^n*exp(-Pi/4)) * 4^n/Pi^(n+1). - _Vaclav Kotesovec_, Sep 29 2013
%F A084098 a(n) = i*((4i)^n*EulerE(n,-i/4)-1)/2. - _Benedict W. J. Irwin_, May 26 2016
%F A084098 a(n) = (i/2)*( -1 + (2*i)^n * Sum_{j=0..n} binomial(n,j)*(-1 - i/2)^j*EulerE(n-j) ). - _G. C. Greubel_, Oct 14 2022
%p A084098 seq(I*((4*I)^n*euler(n,-I/4)-1)/2, n=0..30); # _Robert Israel_, May 26 2016
%t A084098 CoefficientList[Series[E^x*Tan[2*x]/2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 29 2013 *)
%t A084098 Table[I ((4 I)^n*EulerE[n, -I/4] - 1)/2, {n, 0, 20}] (* _Benedict W. J. Irwin_, May 26 2016 *)
%o A084098 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp(x)*Tan(2*x)/2 ))); // _G. C. Greubel_, Oct 14 2022
%o A084098 (SageMath) [(i/2)*(-1 + (2*i)^n*sum(binomial(n,j)*(-1-i/2)^j*euler_number(n-j) for j in range(n+1))) for n in range(40)] # _G. C. Greubel_, Oct 14 2022
%Y A084098 Cf. A009739.
%K A084098 easy,nonn
%O A084098 0,3
%A A084098 _Paul Barry_, May 11 2003