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 A219343 #7 Aug 28 2025 16:58:26
%S A219343 1,1,32,3183,650929,226009218,119298668857,89086101638412,
%T A219343 89480710389500666,116491795770107486363,191172400354899371561288,
%U A219343 387419202671209086703674709,956322827450633453264262285623,2859815748552720894795327258080881,10430012061189048036456303441601971435
%N A219343 O.g.f. satisfies: A(x) = Sum_{n>=0} A(n*x)^n * (n^3*x)^n/n! * exp(-n^3*x*A(n*x)).
%C A219343 Compare to the LambertW identity:
%C A219343 Sum_{n>=0} n^n * x^n * G(x)^n/n! * exp(-n*x*G(x)) = 1/(1 - x*G(x)).
%e A219343 O.g.f.: A(x) = 1 + x + 32*x^2 + 3183*x^3 + 650929*x^4 + 226009218*x^5 +...
%e A219343 where
%e A219343 A(x) = 1 + x*A(x)*exp(-x*A(x)) + 2^6*x^2*A(2*x)^2/2!*exp(-2^3*x*A(2*x)) + 3^9*x^3*A(3*x)^3/3!*exp(-3^3*x*A(3*x)) + 4^12*x^4*A(4*x)^4/4!*exp(-4^3*x*A(4*x)) + 5^15*x^5*A(5*x)^5/5!*exp(-5^3*x*A(5*x)) +...
%e A219343 simplifies to a power series in x with integer coefficients.
%o A219343 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,n,k^(3*k)*x^k*subst(A,x,k*x)^k/k!*exp(-k^3*x*subst(A,x,k*x)+x*O(x^n))));polcoeff(A,n)}
%o A219343 for(n=0,25,print1(a(n),", "))
%Y A219343 Cf. A219264, A219265, A218681, A218672, A219184, A219342, A217900.
%K A219343 nonn,changed
%O A219343 0,3
%A A219343 _Paul D. Hanna_, Nov 18 2012