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 A221409 #8 Jan 15 2013 18:37:23
%S A221409 1,1,1,3,16,117,1185,16856,334597,9263497,360493767,19836684505,
%T A221409 1547142671748,171456480498151,27060184630906514,6089195353964497464,
%U A221409 1955550547239382775017,897232469707513867626376,588505259787507511336381953,552133036731399028180043225074
%N A221409 O.g.f. satisfies: A(x) = Sum_{n>=0} (n-1)^n * x^n * A(n*x)^n/n! * exp(-(n-1)*A(n*x)).
%C A221409 Compare to the LambertW identity:
%C A221409 Sum_{n>=0} (n-1)^n * x^n * G(x)^n/n! * exp(-(n-1)*x*G(x)) = 1/(1 - x*G(x)).
%e A221409 O.g.f.: A(x) = 1 + x + x^2 + 3*x^3 + 16*x^4 + 117*x^5 + 1185*x^6 +...
%e A221409 where
%e A221409 A(x) = exp(x) + 0*x*A(x)*exp(-0*x*A(x)) + 1^2*x^2*A(2*x)^2/2!*exp(-1*x*A(2*x)) + 2^3*x^3*A(3*x)^3/3!*exp(-2*x*A(3*x)) + 3^4*x^4*A(4*x)^4/4!*exp(-3*x*A(4*x)) + 4^5*x^5*A(5*x)^5/5!*exp(-4*x*A(5*x)) +...
%e A221409 simplifies to a power series in x with integer coefficients.
%o A221409 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, (k-1)^k*x^k*subst(A, x, k*x)^k/k!*exp(-(k-1)*x*subst(A, x, k*x)+x*O(x^n)))); polcoeff(A, n)}
%o A221409 for(n=0, 20, print1(a(n), ", "))
%Y A221409 Cf. A218672, A193363, A221410, A221411, A221412, A221413.
%K A221409 nonn
%O A221409 0,4
%A A221409 _Paul D. Hanna_, Jan 15 2013