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 A219265 #7 Jan 13 2025 14:12:21
%S A219265 1,1,8,160,6918,609469,106947753,37651271215,26931993643529,
%T A219265 39243099256414069,116654228928308598913,710224935200206160129234,
%U A219265 8867331728829780268501045551,227187317486051730833557991305666,11969414396907448200529521385052444890
%N A219265 O.g.f. satisfies: A(x) = Sum_{n>=0} A(n^2*x)^n * (n^2*x)^n/n! * exp(-n^2*x*A(n^2*x)).
%C A219265 Compare to the LambertW identity:
%C A219265 Sum_{n>=0} n^n * x^n * G(x)^n/n! * exp(-n*x*G(x)) = 1/(1 - x*G(x)).
%e A219265 O.g.f.: A(x) = 1 + x + 8*x^2 + 160*x^3 + 6918*x^4 + 609469*x^5 +...
%e A219265 where
%e A219265 A(x) = 1 + x*A(x)*exp(-x*A(x)) + 2^4*x^2*A(2^2*x)^2/2!*exp(-2^2*x*A(2^2*x)) + 3^6*x^3*A(3^2*x)^3/3!*exp(-3^2*x*A(3^2*x)) + 4^8*x^4*A(4^2*x)^4/4!*exp(-4^2*x*A(4^2*x)) + 5^10*x^5*A(5^2*x)^5/5!*exp(-5^2*x*A(5^2*x)) +...
%e A219265 simplifies to a power series in x with integer coefficients.
%o A219265 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,n,k^(2*k)*x^k*subst(A,x,k^2*x)^k/k!*exp(-k^2*x*subst(A,x,k^2*x)+x*O(x^n))));polcoeff(A,n)}
%o A219265 for(n=0,25,print1(a(n),", "))
%Y A219265 Cf. A219264, A218681, A218672, A219184, A217900.
%K A219265 nonn
%O A219265 0,3
%A A219265 _Paul D. Hanna_, Nov 16 2012