A163133 G.f. A(x) equals the composition of functions x*(1 + a(n)*x^n); let F_1(x) = x, F_{n+1}(x) = x*(1 + a(n)*F_n(x)^n), then A(x) = limit F_n(x): A(x) = ...o x*(1+a(n)*x^n) o...o x*(1+a(2)*x^2) o x*(1+a(1)*x).

1, 1, 1, 4, 11, 42, 196, 988, 5314, 30724, 189962, 1244264, 8583042, 62112639, 469917193, 3707053139, 30421506639, 259182853643, 2288352779166, 20904648990227, 197305045507448, 1921509079008868, 19285642292478101

Offset

1,4

Links

Table of n, a(n) for n=1..23.

Example

G.f.: A(x) = x + x^2 + x^3 + 4*x^4 + 11*x^5 + 42*x^6 + 196*x^7 +...
A(x) = ...o x*(1+11*x^5) o x*(1+4*x^4) o x*(1+x^3) o x*(1+x^2) o x*(1+x).

Prog

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

Crossrefs

Cf. A119472 (variant).

Sequence in context: A149277 A149278 A176645 * A176574 A323792 A241584

Adjacent sequences: A163130 A163131 A163132 * A163134 A163135 A163136

Keyword

nonn

Author

Paul D. Hanna, Aug 10 2009

Status

approved