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 ...

1, 1, 1, 3, 5, 15, 42, 124, 352, 1124, 3574, 11588, 38033, 127297, 426302, 1459632, 4986161, 17345028, 60373874, 212488958, 747271311, 2661073611, 9451241495, 33925353554, 121618969926, 439680022154, 1586931378911, 5775629048634

Offset

1,4

Links

Table of n, a(n) for n=1..28.

Example

G.f.: A(x) is the limit of the composition of x(1+a(n)*x^n):
F_3(x) = 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+3x^5)) = x + x^2 + x^3 + 3*x^4 + 5*x^5 + 10*x^6 +...
F_6(x) = F_5(x+5x^6) = x + x^2 + x^3 + 3*x^4 + 5*x^5 + 15*x^6 +...
F_7(x) = x+1x^2 o x+1x^3 o x+1x^4 o x+3x^5 o x+5x^6 o x+15x^7 =
x + x^2 + x^3 + 3*x^4 + 5*x^5 + 15*x^6 + 42*x^7 + 82*x^8 +...

Prog

(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)))}

Crossrefs

Cf. A119470, A119471, A119459, A119460.

Sequence in context: A161703 A018551 A103425 * A018568 A371903 A038375

Adjacent sequences: A119469 A119470 A119471 * A119473 A119474 A119475

Keyword

nonn

Author

Paul D. Hanna, May 22 2006

Status

approved