cp's OEIS Frontend

A119470 G.f. A(x) equals the limit of the composition of functions (x+x^n); let F_1(x) = x, F_{n+1}(x) = F_n(x+x^(n+1)), then A(x) = limit F_n(x): A(x) = x o x+x^2 o x+x^3 o ... o x+x^n o...

%I A119470 #8 Nov 28 2023 11:05:57
%S A119470 1,1,1,3,3,7,14,19,37,70,128,195,382,671,1188,2143,3550,6519,11544,
%T A119470 20263,35316,62302,108272,191277,336749,583438,1022109,1784180,
%U A119470 3115162,5411730,9454962,16420712,28558546,49616719,86004273,149312549
%N A119470 G.f. A(x) equals the limit of the composition of functions (x+x^n); let F_1(x) = x, F_{n+1}(x) = F_n(x+x^(n+1)), then A(x) = limit F_n(x): A(x) = x o x+x^2 o x+x^3 o ... o x+x^n o...
%H A119470 Paul D. Hanna, <a href="/A119470/b119470.txt">Table of n, a(n) for n = 1..500</a>
%e A119470 G.f.: A(x) is the limit of the composition of functions (x+x^n):
%e A119470 F_3(x) = x o x+x^2 o x+x^3 = x + x^2 + x^3 + 2*x^4 + x^6;
%e A119470 F_4(x) = F_3(x+x^4) = x + x^2 + x^3 + 3*x^4 + 2*x^5 + 4*x^6 +...
%e A119470 F_5(x) = F_4(x+x^5) = x + x^2 + x^3 + 3*x^4 + 3*x^5 + 6*x^6 +...
%e A119470 F_6(x) = F_5(x+x^6) = x + x^2 + x^3 + 3*x^4 + 3*x^5 + 7*x^6 +...
%e A119470 F_7(x) = x o x+x^2 o x+x^3 o x+x^4 o x+x^5 o x+x^6 o x+x^7 =
%e A119470 x + x^2 + x^3 + 3*x^4 + 3*x^5 + 7*x^6 + 14*x^7 + 18*x^8 +...
%o A119470 (PARI) {a(n)=local(F=x);if(n<1,0,for(k=2,n, F=subst(F,x,x+x^k+x*O(x^n)););return(polcoeff(F,n)))}
%o A119470 for(n=1,60,print1(a(n),", "))
%Y A119470 Cf. A119471, A119472, A119459, A119460.
%K A119470 nonn
%O A119470 1,4
%A A119470 _Paul D. Hanna_, May 22 2006