A120567 G.f. A(x) satisfies: A(x) = x + x*A(x) + x^2*A(A(x)) + x^3*A(A(A(x))) +...

1, 1, 2, 5, 15, 53, 215, 976, 4859, 26150, 150585, 920910, 5946929, 40369352, 287020631, 2130932767, 16478548793, 132438164617, 1104141400679, 9532801486793, 85102769453094, 784511536839904, 7458380835336557

Offset

1,3

Comments

Equals row sums and column 1 of triangle A120568 of self-compositions of A(x).

Links

Paul D. Hanna, Table of n, a(n) for n = 1..200

Example

The successive self-compositions of the g.f. A(x) begin:
A(x) = x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 53*x^6 + 215*x^7 + 976*x^8+...
A(A(x)) = x + 2*x^2 + 6*x^3 + 21*x^4 + 82*x^5 + 351*x^6 + 1630*x^7 +...
A(A(A(x))) = x + 3*x^2 + 12*x^3 + 54*x^4 + 263*x^5 + 1364*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 + 20*x^3 + 110*x^4 + 644*x^5 + 3956*x^6 +...
A(A(A(A(A(x))))) = x + 5*x^2 + 30*x^3 + 195*x^4 + 1335*x^5 +9505*x^6+...
These g.f.s form the columns of triangle A120568.

Prog

(PARI) {a(n)=local(F=x+x*O(x^n), G=F, H=x); for(m=1, n, for(k=1, m, G=subst(F, x, G); H=H+x^k*truncate(G) +x*O(x^n)); F=H; G=x+x^2*O(x^m); H=G; ); polcoeff(F, n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A120568.

Sequence in context: A007548 A360052 A328431 * A263779 A328432 A337850

Adjacent sequences: A120564 A120565 A120566 * A120568 A120569 A120570

Keyword

nonn

Author

Paul D. Hanna, Jun 14 2006

Status

approved