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 A189392 #30 Jan 19 2019 15:34:25
%S A189392 0,1,2,14,88,856,8912,115184,1644928,26916736,484527872,9646440704,
%T A189392 208891091968,4908327894016,124094242629632,3363100573005824,
%U A189392 97195058375262208,2984961531977629696,97056253813754888192,3331252527903082348544
%N A189392 E.g.f. tan(x)/(1-tan(x)-tan(x)^2).
%H A189392 Vincenzo Librandi, <a href="/A189392/b189392.txt">Table of n, a(n) for n = 0..65</a> (corrected by Ray Chandler, Jan 19 2019)
%F A189392 E.g.f.: A(tan(x)) where A(x) = x/(1-x-x^2) is the g.f. of A000045.
%F A189392 a(n)=sum(k=1..n, (sum(i=ceiling((k-1)/2)..k-1, binomial(i,k-i-1)))*((-1)^(n-k)+1)*sum(j=k..n, binomial(j-1,k-1)*j!*2^(n-j-1)*(-1)^((n+k)/2+j)*stirling2(n,j)));
%F A189392 From _Peter Bala_, Mar 12 2013: (Start)
%F A189392 With an offset of -1 the e.g.f is 1/(cos(2*x) - 1/2*sin(2*x))^2 = 1 + 2*x + 14*x^2/2! + 88*x^3/3! + .... This relates this sequence to A185896. Define a sequence of polynomials R(n,x) by the recurrence R(n+1,x) = d/dx{(x^2 + 4)*R(n,x)} with R(1,x) = 1. Then a(n) = R(n,1). Let M be the array with the sequence [2,3,4,...] on the main superdiagonal and the sequence [4,8,12,...] on the main subdiagonal and 0's everywhere else. Then a(n+1) equals the sum of the entries in row 1 of M^n.
%F A189392 (End)
%F A189392 a(n) ~ n! / (5*(arctan(sqrt(5)/2-1/2))^(n+1)). - _Vaclav Kotesovec_, Jun 02 2013
%F A189392 G.f.: x/Q(0), where Q(k) = 1 - 2*x*(2*k+1) - 5*x^2*(2*k+1)*(2*k+2)/( 1 - 2*x*(2*k+2) - 5*x^2*(2*k+2)*(2*k+3)/Q(k+1) ) ; (continued fraction). - _Sergei N. Gladkovskii_, Sep 23 2013
%F A189392 E.g.f.: W(0) -1, where W(k) = 1 + x/( 4*k+1 - x/( 1 - 4*x/( 4*k+3 + 4*x/W(k+1) ))); (continued fraction). - _Sergei N. Gladkovskii_, Oct 27 2014
%e A189392 G.f. = x + 2*x^2 + 14*x^3 + 88*x^4 + 856*x^5 + 8912*x^6 + 115184*x^7 + ...
%t A189392 nn = 20; Range[0, nn]! CoefficientList[Series[Tan[x]/(1 - Tan[x] - Tan[x]^2), {x, 0, nn}], x] (* _T. D. Noe_, Mar 14 2013 *)
%o A189392 (Maxima)
%o A189392 a(n):=sum((sum(binomial(i,k-i-1),i,ceiling((k-1)/2),k-1))*((-1)^(n-k)+1)*sum(binomial(j-1,k-1)*j!*2^(n-j-1)*(-1)^((n+k)/2+j)*stirling2(n,j),j,k,n),k,1,n);
%o A189392 (PARI) x='x+O('x^66); /* that many terms */
%o A189392 egf=tan(x)/(1-tan(x)-tan(x)^2); /* = x + x^2 + 7/3*x^3 + 11/3*x^4 +... */
%o A189392 Vec(serlaplace(egf)) /* _Joerg Arndt_, Apr 22 2011 */
%Y A189392 Cf. A185896.
%K A189392 nonn
%O A189392 0,3
%A A189392 _Vladimir Kruchinin_, Apr 21 2011