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 A213110 #10 Oct 27 2024 04:16:08
%S A213110 1,1,5,61,1089,29081,1006753,44229669,2338846849,145278355825,
%T A213110 10340497436481,829144792315709,73858518558797569,7228342584930637353,
%U A213110 770235745321038739681,88690109534418912004501,10965585032265975064491777,1447844650991790389918127329
%N A213110 E.g.f.: A(x) = exp( x/A(-x*A(x)^5)^2 ).
%C A213110 Compare the e.g.f. to:
%C A213110 (1) W(x) = exp(x/W(-x*W(x)^2)^1) when W(x) = Sum_{n>=0} (1*n+1)^(n-1)*x^n/n!.
%C A213110 (2) W(x) = exp(x/W(-x*W(x)^4)^2) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.
%C A213110 (3) W(x) = exp(x/W(-x*W(x)^6)^3) when W(x) = Sum_{n>=0} (3*n+1)^(n-1)*x^n/n!.
%e A213110 E.g.f.: A(x) = 1 + x + 5*x^2/2! + 61*x^3/3! + 1089*x^4/4! + 29081*x^5/5! +...
%e A213110 Related expansions:
%e A213110 A(x)^2 = 1 + 2*x + 12*x^2/2! + 152*x^3/3! + 2816*x^4/4! + 75152*x^5/5! +...
%e A213110 A(x)^5 = 1 + 5*x + 45*x^2/2! + 665*x^3/3! + 13745*x^4/4! + 380525*x^5/5! +...
%e A213110 1/A(-x*A(x)^5)^2 = 1 + 2*x + 16*x^2/2! + 206*x^3/3! + 4456*x^4/4! +...
%e A213110 The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^5)^2, begins:
%e A213110 log(A(x)) = x + 4*x^2/2! + 48*x^3/3! + 824*x^4/4! + 22280*x^5/5! + 774012*x^6/6! +...
%o A213110 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(x/subst(A^2,x,-x*A^5+x*O(x^n))));n!*polcoeff(A,n)}
%o A213110 for(n=0,25,print1(a(n),", "))
%Y A213110 Cf. A213108, A213109, A213111, A213112, A213113.
%K A213110 nonn
%O A213110 0,3
%A A213110 _Paul D. Hanna_, Jun 05 2012