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 A221412 #5 Jan 15 2013 18:36:12
%S A221412 1,1,5,39,576,11693,358649,15411564,951579001,83392989241,
%T A221412 10419431480203,1856210104355977,471536928543684056,
%U A221412 170959559745467848287,88469465053214549982042,65371115770077488407503980,68993903807593031325051425205,104033290140443202579946504758992
%N A221412 O.g.f. satisfies: A(x) = Sum_{n>=0} (n+3)^n * x^n * A(n*x)^n/n! * exp(-(n+3)*x*A(n*x)).
%C A221412 Compare to the LambertW identity:
%C A221412 Sum_{n>=0} (n+3)^n * x^n * G(x)^n/n! * exp(-(n+3)*x*G(x)) = 1/(1 - x*G(x)).
%e A221412 O.g.f.: A(x) = 1 + x + 5*x^2 + 39*x^3 + 576*x^4 + 11693*x^5 + 358649*x^6 +...
%e A221412 where
%e A221412 A(x) = exp(-3*x) + 4*x*A(x)*exp(-4*x*A(x)) + 5^2*x^2*A(2*x)^2/2!*exp(-5*x*A(2*x)) + 6^3*x^3*A(3*x)^3/3!*exp(-6*x*A(3*x)) + 7^4*x^4*A(4*x)^4/4!*exp(-7*x*A(4*x)) + 8^5*x^5*A(5*x)^5/5!*exp(-8*x*A(5*x)) +...
%e A221412 simplifies to a power series in x with integer coefficients.
%o A221412 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, (k+3)^k*x^k*subst(A, x, k*x)^k/k!*exp(-(k+3)*x*subst(A, x, k*x)+x*O(x^n)))); polcoeff(A, n)}
%o A221412 for(n=0, 20, print1(a(n), ", "))
%Y A221412 Cf. A218672, A193363, A221409, A221410, A221411, A221413.
%K A221412 nonn
%O A221412 0,3
%A A221412 _Paul D. Hanna_, Jan 15 2013