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 A232691 #9 Jan 05 2014 11:23:29
%S A232691 1,1,3,19,161,1857,25843,433891,8378913,185022049,4565674115,
%T A232691 125075024211,3755498096257,122872235056993,4345683577199283,
%U A232691 165338206044981091,6730088764152273857,291935651271257092161,13440846879808207921027,654704450541594973156627
%N A232691 E.g.f. satisfies: A(x) = exp( 1/A(x)^2 * Integral A(x)^6 dx ).
%C A232691 Note that G(x) = exp(1/G(x)^2 * Integral G(x)^5 dx) has negative coefficients.
%C A232691 Compare e.g.f. to: B(x) = exp( 1/B(x)^2 * Integral B(x)^2 dx ) where B(y) = Bessel polynomial y_n(-2) (cf. A002119).
%F A232691 E.g.f.: (LambertW(-1, (8*x-3)*exp(-3))/(8*x-3))^(1/4). - _Vaclav Kotesovec_, Jan 05 2014
%e A232691 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 161*x^4/4! + 1857*x^5/5! +...
%e A232691 Related expansions:
%e A232691 log(A(x)) = x + 2*x^2/2! + 12*x^3/3! + 88*x^4/4! + 976*x^5/5! + 12576*x^6/6! +...
%e A232691 Integral A(x)^6 dx = x + 6*x^2/2! + 48*x^3/3! + 504*x^4/4! + 6576*x^5/5! +...
%e A232691 1/A(x)^2 = 1 - 2*x - 8*x^3/3! - 16*x^4/4! - 384*x^5/5! - 2624*x^6/6! -...
%p A232691 seq(n! * coeff(series((LambertW(-1, (8*x-3)*exp(-3))/(8*x-3))^(1/4), x, n+1), x, n), n=0..20) # _Vaclav Kotesovec_, Jan 05 2014
%o A232691 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(1/A^2*intformal(A^6+x*O(x^n))));n!*polcoeff(A,n)}
%o A232691 for(n=0,30,print1(a(n),", "))
%Y A232691 Cf. A232690, A232692.
%K A232691 nonn
%O A232691 0,3
%A A232691 _Paul D. Hanna_, Dec 06 2013