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...

1, 1, 1, 3, 3, 7, 14, 19, 37, 70, 128, 195, 382, 671, 1188, 2143, 3550, 6519, 11544, 20263, 35316, 62302, 108272, 191277, 336749, 583438, 1022109, 1784180, 3115162, 5411730, 9454962, 16420712, 28558546, 49616719, 86004273, 149312549

Offset: 1

Author

Paul D. Hanna, May 22 2006

Keywords

• nonn

Examples

			G.f.: A(x) is the limit of the composition of functions (x+x^n):
F_3(x) = x o x+x^2 o x+x^3 = x + x^2 + x^3 + 2*x^4 + x^6;
F_4(x) = F_3(x+x^4) = x + x^2 + x^3 + 3*x^4 + 2*x^5 + 4*x^6 +...
F_5(x) = F_4(x+x^5) = x + x^2 + x^3 + 3*x^4 + 3*x^5 + 6*x^6 +...
F_6(x) = F_5(x+x^6) = x + x^2 + x^3 + 3*x^4 + 3*x^5 + 7*x^6 +...
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 =
x + x^2 + x^3 + 3*x^4 + 3*x^5 + 7*x^6 + 14*x^7 + 18*x^8 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A119471, A119472, A119459, A119460.

Programs

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)))}
for(n=1,60,print1(a(n),", "))