cp's OEIS Frontend

A119472 G.f. A(x) equals the composition of functions x*(1 + a(n)*x^n); let F_1(x) = x, F_{n+1}(x) = F_n( x*(1 + a(n)*x^n) ), then A(x) = limit F_n(x): A(x) = x*(1+a(1)*x) o x*(1+a(2)*x^2) o ... o x*(1+a(n)*x^n) o ...

%I A119472 #8 Jan 25 2025 02:12:59
%S A119472 1,1,1,3,5,15,42,124,352,1124,3574,11588,38033,127297,426302,1459632,
%T A119472 4986161,17345028,60373874,212488958,747271311,2661073611,9451241495,
%U A119472 33925353554,121618969926,439680022154,1586931378911,5775629048634
%N A119472 G.f. A(x) equals the composition of functions x*(1 + a(n)*x^n); let F_1(x) = x, F_{n+1}(x) = F_n( x*(1 + a(n)*x^n) ), then A(x) = limit F_n(x): A(x) = x*(1+a(1)*x) o x*(1+a(2)*x^2) o ... o x*(1+a(n)*x^n) o ...
%e A119472 G.f.: A(x) is the limit of the composition of x*(1+a(n)*x^n):
%e A119472 F_3(x) = x+x^2 o x+x^3 = x + x^2 + x^3 + 2*x^4 + x^6;
%e A119472 F_4(x) = F_3(x+x^4) = x + x^2 + x^3 + 3*x^4 + 2*x^5 + 4*x^6 +...
%e A119472 F_5(x) = F_4(x+3*x^5) = x + x^2 + x^3 + 3*x^4 + 5*x^5 + 10*x^6 +...
%e A119472 F_6(x) = F_5(x+5*x^6) = x + x^2 + x^3 + 3*x^4 + 5*x^5 + 15*x^6 +...
%e A119472 F_7(x) = x+1*x^2 o x+1*x^3 o x+1*x^4 o x+3*x^5 o x+5*x^6 o x+15*x^7 =
%e A119472          x + x^2 + x^3 + 3*x^4 + 5*x^5 + 15*x^6 + 42*x^7 + 82*x^8 +...
%o A119472 (PARI) {a(n)=local(F=x);if(n<1,0,for(k=2,n, F=subst(F,x,x+a(k-1)*x^k +x*O(x^n)););return(polcoeff(F,n)))}
%Y A119472 Cf. A119470, A119471, A119459, A119460.
%K A119472 nonn
%O A119472 1,4
%A A119472 _Paul D. Hanna_, May 22 2006