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 A007836 #49 Dec 17 2021 05:28:29
%S A007836 1,1,1,5,23,151,1141,10205,103823,1190191,15151981,212222405,
%T A007836 3242472023,53670028231,956685677221,18271360434605,372221031054623,
%U A007836 8056751598834271,184647141575344861,4466900836910758805
%N A007836 Springer numbers associated with symplectic group.
%C A007836 Comments from _F. Chapoton_, Oct 30 2009: To compute this sequence, I used something similar to the Boustrophedon definition of the Euler numbers, but with two triangles instead of one. This is described (page 94) in Arnold's article in "Leçons de mathématiques d'aujourd'hui, volume 1" Editions Cassini. This is very similar to A001586, except that the initial conditions ( (0,1) at top of the two triangles ) are exchanged.
%D A007836 V. I. Arnold, The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups, Uspekhi Mat. Nauk., 47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51.
%D A007836 V. I. Arnold, Nombres d'Euler, de Bernoulli et de Springer pour les groupes de Coxeter et les espaces de morsification : le calcul des serpents, in "Leçons de mathématiques d'aujourd'hui, volume 1", Editions Cassini.
%H A007836 Vincenzo Librandi, <a href="/A007836/b007836.txt">Table of n, a(n) for n = 0..200</a>
%H A007836 Michael E. Hoffman, <a href="https://doi.org/10.37236/1453">Derivative Polynomials, Euler Polynomials, and Associated Integer Sequences</a>, The Electronic Journal of Combinatorics, Volume 6.1 (1999): Research paper R21, 13 p.
%H A007836 M. Josuat-Verges, J.-C. Novelli and J.-Y. Thibon, <a href="http://arxiv.org/abs/1110.5272">The algebraic combinatorics of snakes</a>, arXiv preprint arXiv:1110.5272 [math.CO], 2011.
%H A007836 A. Vieru, <a href="http://arxiv.org/abs/1107.2938">Agoh's conjecture: its proof, its generalizations, its analogues</a>, arXiv preprint arXiv:1107.2938 [math.NT], 2011-2012.
%F A007836 a(n) = P_n(1) - Q_n(1) (see A155100 and A104035), defining Q_{-1} = 0. Cf. A156142.
%F A007836 From _Vaclav Kotesovec_, Dec 08 2020: (Start)
%F A007836 E.g.f.: (2*cos(x) - 1) / (cos(x) - sin(x)).
%F A007836 a(n) ~ (2 - sqrt(2)) * 2^(2*n + 3/2) * n^(n + 1/2) / (Pi^(n + 1/2) * exp(n)). (End)
%t A007836 p[n_, u_] := D[Tan[x], {x, n}] /. Tan[x] -> u /. Sec[x] -> Sqrt[1+u^2] // Expand; p[-1, u_] = 1; t[n_, k_] := t[n, k] = k*t[n-1, k-1]+(k+1)*t[n-1, k+1]; t[0, 0] = 1; t[0, _] = 0; t[-1, _] = 0; q[n_, u_] := Sum[t[n, k]*u^k, {k, 0, n}]; a[n_] := p[n, 1]-q[n, 1]; a[0]=1; Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Feb 05 2014 *)
%t A007836 nmax = 20; CoefficientList[Series[1 + (Sin[x] + Cos[x] - 1) / (Cos[x] - Sin[x]), {x, 0, nmax}], x] * Range[0,nmax]! (* _Vaclav Kotesovec_, Dec 08 2020 *)
%Y A007836 Cf. A001586, A155100, A104035, A156142.
%K A007836 nonn,nice
%O A007836 0,4
%A A007836 _N. J. A. Sloane_
%E A007836 More terms from _F. Chapoton_, Oct 30 2009