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A120567 G.f. A(x) satisfies: A(x) = x + x*A(x) + x^2*A(A(x)) + x^3*A(A(A(x))) +... 2
1, 1, 2, 5, 15, 53, 215, 976, 4859, 26150, 150585, 920910, 5946929, 40369352, 287020631, 2130932767, 16478548793, 132438164617, 1104141400679, 9532801486793, 85102769453094, 784511536839904, 7458380835336557 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

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(i=1, n, for(k=1, n, G=subst(F, x, G); H=H+x^k*G); F=H; G=x+x*O(x^n); H=G); polcoeff(F, n)}

CROSSREFS

Cf. A120568.

Sequence in context: A249892 A006790 A007548 * A263779 A125280 A022493

Adjacent sequences:  A120564 A120565 A120566 * A120568 A120569 A120570

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 14 2006

STATUS

approved

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Last modified October 13 19:35 EDT 2019. Contains 327981 sequences. (Running on oeis4.)