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 A223076 #5 Mar 14 2013 13:07:29
%S A223076 1,1,3,25,433,14929,1009039,134378493,35413549073,18529994604561,
%T A223076 19287258947192299,39990414610486392193,165330456559779835205073,
%U A223076 1363910437230335758822062353,22464490025153709857947688719687,739043653017364758151896078253911765
%N A223076 O.g.f. satisfies: A(x) = Sum_{n>=0} n^n * x^n * A(2*n*x)^n/n! * exp(-n*x*A(2*n*x)).
%C A223076 Compare to the LambertW identity:
%C A223076 Sum_{n>=0} n^n * x^n * G(x)^n/n! * exp(-n*x*G(x)) = 1/(1 - x*G(x)).
%F A223076 a(4*n+2) == 3 (mod 4) for n>=0; a(n) == 1 (mod 2) for n>=0.
%e A223076 O.g.f.: A(x) = 1 + x + 3*x^2 + 25*x^3 + 433*x^4 + 14929*x^5 + 1009039*x^6 +...
%e A223076 where
%e A223076 A(x) = 1 + x*A(2*x)*exp(-x*A(2*x)) + 2^2*x^2*A(4*x)^2/2!*exp(-2*x*A(4*x)) + 3^3*x^3*A(6*x)^3/3!*exp(-3*x*A(6*x)) + 4^4*x^4*A(8*x)^4/4!*exp(-4*x*A(8*x)) + 5^5*x^5*A(10*x)^5/5!*exp(-5*x*A(10*x)) +...
%e A223076 simplifies to a power series in x with integer coefficients.
%o A223076 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, k^k*x^k*subst(A, x, 2*k*x)^k/k!*exp(-k*x*subst(A, x, 2*k*x)+x*O(x^n)))); polcoeff(A, n)}
%o A223076 for(n=0, 20, print1(a(n), ", "))
%Y A223076 Cf. A223075, A218672, A217900.
%K A223076 nonn
%O A223076 0,3
%A A223076 _Paul D. Hanna_, Mar 14 2013