A141117 G.f.: A(x) = G(G(x)) = G(x)*[1 + A(A(x))] where G(x) = x + x*G(G(G(x))) = g.f. of A091713.

1, 2, 8, 46, 330, 2756, 25782, 263866, 2909092, 34181138, 424730866, 5549236120, 75895955810, 1082808876274, 16069706031016, 247501424330182, 3948322598675930, 65130737179097436, 1109339652229852966

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

G.f. A(x) satisfies: G( x/(1 + A(x)) ) = x where G(x) = g.f. of A091713.

Example

G.f.: A(x) = G(G(x)) such that G(x) = A(x)/[1 + A(A(x))] where
G(x) = x + x^2 + 3*x^3 + 15*x^4 + 99*x^5 + 781*x^6 + 7001*x^7 +...
A(x) = x + 2*x^2 + 8*x^3 + 46*x^4 + 330*x^5 + 2756*x^6 + 25782*x^7 +...
A(A(x)) = x + 4*x^2 + 24*x^3 + 180*x^4 + 1564*x^5 + 15140*x^6 +...

Prog

(PARI) {a(n)=local(A); A=x+x^2; for(i=3, n, A=x+x*subst(A, x, subst(A, x, A))+x*O(x^n)); polcoeff(subst(A, x, A), n, x)}

Crossrefs

Cf. A091713.

Sequence in context: A326351 A276358 A337060 * A145844 A005840 A161881

Adjacent sequences: A141114 A141115 A141116 * A141118 A141119 A141120

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2008

Status

approved