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 A143599 #11 Feb 26 2014 06:32:16
%S A143599 1,1,3,10,53,316,2527,22072,239689,2774800,38284091,553477024,
%T A143599 9284250109,161180444608,3187413648343,64638167906176,
%U A143599 1473221217774353,34190645940363520,882759869810501491,23079229227696318976
%N A143599 E.g.f. satisfies: A(x) = exp( x*sqrt(A(x)/A(-x)) ).
%H A143599 Vaclav Kotesovec, <a href="/A143599/b143599.txt">Table of n, a(n) for n = 0..218</a>
%F A143599 E.g.f.: A(x) = exp(x*exp(x*G(x))) where G(x) = cosh(x*G(x)) = e.g.f. of A143601.
%F A143599 E.g.f.: sqrt(A(x)/A(-x)) = F(x) = exp(x*[F(x) + 1/F(x)]/2) = e.g.f. of A058014.
%F A143599 E.g.f.: [sqrt(A(x)/A(-x)) + sqrt(A(-x)/A(x))]/2 = e.g.f. of A143601.
%F A143599 E.g.f.: [sqrt(A(x)/A(-x)) - sqrt(A(-x)/A(x))]/2 = e.g.f. of A007106.
%F A143599 E.g.f.: A(x) = H(x/2)^2 where H(x) = exp(x*H(x)/H(-x)) = e.g.f. of A143600.
%F A143599 E.g.f. satisfies: A(x/cosh(x)) = exp(x*exp(x)/cosh(x)). [From _Paul D. Hanna_, Aug 29 2008]
%F A143599 E.g.f. satisfies: -x*sqrt(x^2/log(y)^2) = log((x^2*y)/log(y)^2), where y=A(x). - _Vaclav Kotesovec_, Feb 26 2014
%F A143599 a(n) ~ c * n! * d^n / n^(3/2), where d = 1.5088795615383199289... is the root of the equation sqrt(1+1/d^2) = 1 + LambertW((1+sqrt(1+1/d^2))/exp(1 + sqrt(1+1/d^2))), and c = 7.98255033020099890281693169... if n is even, and c = 7.852067808737280621088934789... if n is odd. - _Vaclav Kotesovec_, Feb 26 2014
%e A143599 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 53*x^4/4! + 316*x^5/5! +...
%e A143599 F(x) = sqrt(A(x)/A(-x)) = e.g.f. of A058014:
%e A143599 F(x) = 1 + x + 1*x^2/2! + 4*x^3/3! + 13*x^4/4! + 96*x^5/5! + 541*x^6/6! +...
%e A143599 where F(x) = exp(x*(F(x) + 1/F(x))/2).
%e A143599 G(x) = [sqrt(A(x)/A(-x)) + sqrt(A(-x)/A(x))]/2 = e.g.f. of A143601:
%e A143599 G(x) = 1 + x^2/2! + 13*x^4/4! + 541*x^6/6! + 47545*x^8/8! +...
%e A143599 where G(x) = cosh(x*G(x)).
%e A143599 S(x) = [sqrt(A(x)/A(-x)) - sqrt(A(-x)/A(x))]/2 = e.g.f. of A007106:
%e A143599 S(x) = x + 4*x^3/3! + 96*x^5/5! + 5888*x^7/7! + 686080*x^9/9! +...
%e A143599 where S(x) = sqrt(G(x)^2 - 1) and G(x) = e.g.f. of A143601.
%o A143599 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=exp(x*sqrt(A/subst(A,x,-x))));n!*polcoeff(A,n)}
%Y A143599 Cf. A058014, A143600, A143601, A007106.
%K A143599 nonn
%O A143599 0,3
%A A143599 _Paul D. Hanna_, Aug 27 2008