sequences from Hilbert's 16th problem?

[N. J. A. Sloane]

Dear Math-Fun and Seqfans,

In his 2002 survey,

MR1898209 (2003c:34001) Ilyashenko, Yu. Centennial history of Hilbert's 16th problem.  Bull. Amer. Math. Soc. (N.S.)  39  (2002),  no. 3, 301--354 (electronic). (Reviewer: Lubomir Gavrilov) 34-02 (34C07 37C10 37F75)

the author mentions that Petrovskii and Landis gave an incorrect proof that
the Hilbert number H(n) is bounded above by P_3(n), "a certain polynomial
of degree 3 [in n]".  The reference is to:

MR0073004 (17,364d)
Petrovski\u\i, I. G.; Landis, E. M.
On the number of limit cycles of the equation $dy/dx=P(x,y)/Q(x,y)$, where $P$ and $Q$ are polynomials of 2nd degree. (Russian)
Mat. Sb. N.S. 37(79) (1955), 209--250.

My question is, what is this sequence P_3(n) ?

Later in the article Ilyashenko mentions a second Hilbert-type
sequence E(n) (on page 305).  Same question.

NJAS