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 A221413 #6 Aug 22 2024 16:43:43
%S A221413 1,1,6,53,931,21847,791525,39781921,2896348222,298603689072,
%T A221413 43979877929712,9234821696038425,2765498896234870783,
%U A221413 1182132922860352133076,721128788569371093881079,628104461090874688307332589,781298529318782688558174387547
%N A221413 O.g.f. satisfies: A(x) = Sum_{n>=0} (n+4)^n * x^n * A(n*x)^n/n! * exp(-(n+4)*x*A(n*x)).
%e A221413 O.g.f.: A(x) = 1 + x + 6*x^2 + 53*x^3 + 931*x^4 + 21847*x^5 + 791525*x^6 +...
%e A221413 where
%e A221413 A(x) = exp(-4*x) + 5*x*A(x)*exp(-5*x*A(x)) + 6^2*x^2*A(2*x)^2/2!*exp(-6*x*A(2*x)) + 7^3*x^3*A(3*x)^3/3!*exp(-7*x*A(3*x)) + 8^4*x^4*A(4*x)^4/4!*exp(-8*x*A(4*x)) + 9^5*x^5*A(5*x)^5/5!*exp(-9*x*A(5*x)) +...
%e A221413 simplifies to a power series in x with integer coefficients.
%o A221413 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, (k+4)^k*x^k*subst(A, x, k*x)^k/k!*exp(-(k+4)*x*subst(A, x, k*x)+x*O(x^n)))); polcoeff(A, n)}
%o A221413 for(n=0, 20, print1(a(n), ", "))
%Y A221413 Cf. A218672, A193363, A221409, A221410, A221411, A221412.
%K A221413 nonn
%O A221413 0,3
%A A221413 _Paul D. Hanna_, Jan 15 2013