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 A193099 #10 Jun 27 2025 16:28:12
%S A193099 1,1,4,34,466,9044,230827,7388781,287044354,13212057907,707417718215,
%T A193099 43431362340153,3022050938855344,236053437141340206,
%U A193099 20532456001485751429,1975258248906891145913,208928124926501980596761,24172548454436633069025270
%N A193099 E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(A(x)))).
%e A193099 E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 34*x^4/4! + 466*x^5/5! + 9044*x^6/6! +...
%e A193099 where the derivative of the e.g.f. begins:
%e A193099 A'(x) = 1 + x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...
%e A193099 Related expansions.
%e A193099 A(A(x)) = x + 2*x^2/2! + 11*x^3/3! + 111*x^4/4! + 1702*x^5/5! + 35854*x^6/6! +...
%e A193099 A(A(A(x))) = x + 3*x^2/2! + 21*x^3/3! + 249*x^4/4! + 4303*x^5/5! + 99650*x^6/6! +...
%e A193099 A(A(A(A(x)))) = x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...
%o A193099 (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(1+subst(A, x, subst(A, x, subst(A, x, A+O(x^(n+1))))))); n!*polcoeff(A, n)}
%Y A193099 Cf. A001028, A193098, A193100, A179420.
%K A193099 nonn
%O A193099 1,3
%A A193099 _Paul D. Hanna_, Jul 15 2011