%I A141358
%S A141358 1,1,7,106,2509,80956,3313579,164514904,9608077945,645470256592,
%T A141358 49038954301711,4157529546929056,389125813949115973,
%U A141358 39853422352958799040,4433527105413108692851,532370587431255626482816
%N A141358 E.g.f.: A(x) = exp(x*A(x)^3*exp(x^2*A(x)^6*exp(x^3*A(x)^9*exp(x^4*A(x)^12*exp(...))))), 
               an infinite power tower.
%F A141358 E.g.f.: A(x) = (1/x)*Series_Reversion(x/C(x)) where C(x) is the e.g.f. 
               of A141357.
%F A141358 E.g.f.: A(x) = x/Series_Reversion(x*D(x)) where D(x) is the e.g.f. of 
               A141359.
%F A141358 E.g.f.: A(x) = B(x*A(x)^2) where B(x) = exp(x*B(x)*exp(x^2*B(x)^2*exp(x^3*B(x)^3*exp(...)))) 
               is the e.g.f. of A141356 = [1,1,3,22,245,3516,63727,1405384,...].
%F A141358 E.g.f.: A(x) = C(x*A(x)) where C(x) = exp(x*C(x)^2*exp(x^2*C(x)^4*exp(x^3*C(x)^6*exp(...)))) 
               is the e.g.f. of A141357 = [1,1,5,55,945,21961,645013,22948815,...].
%F A141358 E.g.f.: A(x) = D(x/A(x)) where D(x) = exp(x*D(x)^4*exp(x^2*D(x)^8*exp(x^3*D(x)^12*exp(...)))) 
               is the e.g.f. of A141359 = [1,1,9,175,5321,221001,11659345,746678311,
               ...].
%e A141358 E.g.f.: A(x) = 1 + x + 7*x^2/2! + 106*x^3/3! + 2509*x^4/4! + 80956*x^5/
               5! +...
%o A141358 (PARI) {a(n)=local(A=1+x,F);for(i=0,n,for(j=0,n,F=exp((x*(A+x*O(x^n))^3)^(n-j+1)*F));
               A=F);n!*polcoeff(A,n)}
%Y A141358 Cf. A141356, A141357, A141359; variant: A141362.
%Y A141358 Sequence in context: A049210 A002486 A145167 this_sequence A141362 A075021 
               A138963
%Y A141358 Adjacent sequences: A141355 A141356 A141357 this_sequence A141359 A141360 
               A141361
%K A141358 nonn
%O A141358 0,3
%A A141358 Paul D. Hanna (pauldhanna(AT)juno.com), Jun 28 2008