A119471 G.f. A(x) equals the limit of the composition of functions (x+x^n) in reverse order; let F_1(x) = x, F_{n+1}(x) = F_n(x) + F_n(x)^(n+1), then A(x) = limit F_n(x): A(x) = ...o x+x^n o ... o x+x^3 o x+x^2 o x.

1, 1, 1, 4, 8, 17, 50, 146, 399, 1087, 3042, 8741, 25509, 75259, 223529, 665215, 1983226, 5931158, 17800505, 53627756, 162206221, 492399027, 1499501067, 4579193127, 14017819056, 43001141630, 132154209754, 406818719006

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+x^3 o x+x^2 o x = x + x^2 + x^3 + 3*x^4 + 3*x^5 + x^6;
F_4(x) = x+x^4 o F_3(x) = x + x^2 + x^3 + 4*x^4 + 7*x^5 + 11*x^6 +...
F_5(x) = x+x^5 o F_4(x) = x + x^2 + x^3 + 4*x^4 + 8*x^5 + 16*x^6 +...
F_6(x) = x+x^6 o F_5(x) = x + x^2 + x^3 + 4*x^4 + 8*x^5 + 17*x^6 +...
F_7(x) = x+x^7 o x+x^6 o x+x^5 o x+x^4 o x+x^3 o x+x^2 o x =
x + x^2 + x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 50*x^7 + 145*x^8 +...
		

Links

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

Crossrefs

Cf. A119470, A119472, A119459, A119460.

Programs

PARI

{a(n)=local(F=x);if(n<1,0,for(k=2,n, F=subst(x+x^k,x,F+x*O(x^n)););return(polcoeff(F,n)))}