A185754 G.f. satisfies: A(x) = x + x*sqrt(A(A(x)) - A(x)).

1, 1, 2, 7, 36, 243, 2016, 19745, 222318, 2824546, 39938124, 621808679, 10569132576, 194745803641, 3866820606006, 82313887902511, 1870203518285750, 45174881008705328, 1156071783429567906, 31246398342838909318

Offset

1,3

Links

Table of n, a(n) for n=1..20.

Formula

Let F(x) be the g.f. of A185753, then g.f. A(x) satisfies:

* A(x) = x + (F(x)-1)^2,

* A(x) = x*F(A(x)),

* A(x) = Series_Reversion(x/F(x)).

Example

 G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 36*x^5 + 243*x^6 +...
A(A(x)) = x + 2*x^2 + 6*x^3 + 25*x^4 + 136*x^5 + 922*x^6 + 7524*x^7 +...
The g.f. of A185753 begins:
F(x) = 1 + x + x^2 + 3*x^3 + 15*x^4 + 102*x^5 + 861*x^6 + 8593*x^7 +...
where
(F(x)-1)^2 = x^2 + 2*x^3 + 7*x^4 + 36*x^5 + 243*x^6 + 2016*x^7 +...
F(A(x)) = 1 + x + 2*x^2 + 7*x^3 + 36*x^4 + 243*x^5 + 2016*x^6 +...

Prog

 (PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=2*A-x-(x/serreverse(A+x*O(x^n))-1)^2); polcoeff(A, n)}

Crossrefs

Cf. A185753.

Sequence in context: A373773 A088313 A201197 * A191493 A095793 A029768

Adjacent sequences: A185751 A185752 A185753 * A185755 A185756 A185757

Keyword

nonn

Author

Paul D. Hanna, Feb 02 2011

Status

approved