A185897 G.f. satisfies: x/(1-x) = A(x - A(x)^2).

1, 2, 9, 64, 574, 5919, 67205, 820258, 10602848, 143710500, 2028137178, 29649220223, 447247229447, 6940546801219, 110540089124381, 1803424905623166, 30092225956558590, 512900050694933194

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

G.f.: A(x) = G(x)/(1 - G(x)) where

* G(x) = A(x)/(1 + A(x)) and

* G(x) = Series_Reversion(x - A(x)^2).

Example

G.f.: A(x) = x + 2*x^2 + 9*x^3 + 64*x^4 + 574*x^5 + 5919*x^6 +...
Related expansions.
x - A(x)^2 = x - x^2 - 4*x^3 - 22*x^4 - 164*x^5 - 1485*x^6 -...
Let G(x) equal the series reversion of x - A(x)^2, then
G(x) = x + x^2 + 6*x^3 + 47*x^4 + 442*x^5 + 4691*x^6 + 54330*x^7 +...
1/(1-G(x)) = 1 + x + 2*x^2 + 9*x^3 + 64*x^4 + 574*x^5 + 5919*x^6 +...

Prog

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

Crossrefs

Sequence in context: A024720 A289717 A094100 * A067297 A274394 A368291

Adjacent sequences: A185894 A185895 A185896 * A185898 A185899 A185900

Keyword

nonn

Author

Paul D. Hanna, Feb 05 2011

Status

approved