A185898 G.f. satisfies: x + x^2 = A(x - A(x)^2).

1, 2, 8, 58, 516, 5264, 59056, 712002, 9091360, 121741316, 1697801200, 24533242088, 365899614704, 5615722652912, 88482403906752, 1428528355241602, 23595413088087220, 398214274587320432, 6859495185702804744

Offset

1,2

Links

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

Formula

G.f.: A(x) = G(x) + G(x)^2 where

* G(x) = (sqrt(1 + 4*A(x)) - 1)/2;

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

Example

G.f.: A(x) = x + 2*x^2 + 8*x^3 + 58*x^4 + 516*x^5 + 5264*x^6 +...
Related expansions.
x - A(x)^2 = x - x^2 - 4*x^3 - 20*x^4 - 148*x^5 - 1328*x^6 -...
Let G(x) equal the series reversion of x - A(x)^2, then
G(x) = x + x^2 + 6*x^3 + 45*x^4 + 414*x^5 + 4310*x^6 + 49068*x^7 +...
G(x)^2 = x^2 + 2*x^3 + 13*x^4 + 102*x^5 + 954*x^6 + 9988*x^7 +...

Prog

(PARI) {a(n)=local(A=x+2*x^2, B=serreverse(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: A007347 A027257 A308352 * A063074 A319590 A005804

Adjacent sequences: A185895 A185896 A185897 * A185899 A185900 A185901

Keyword

nonn

Author

Paul D. Hanna, Feb 05 2011

Status

approved