OFFSET
1,3
COMMENTS
The definition was originally used in A279196, which however happened to additionally require the quotient Q(x,y) = (P(x,y)-1) / (x+y-1) to have nonnegative coefficients as well. The current sequence allows these coefficients be negative. Hence a(n) >= A279196(n).
Let Q_d(x,y) be the homogeneous part of Q(x,y) of degree d, and c_d = Q_d(1,1). Then c_0 = 1, c_1, ... form a sequence of nonnegative integers such that c_d <= 2*c_{d-1} and c_0 + c_1 + ... = n-1 (cf. A002572). It follows that Q(x,y) and P(x,y) have degree at most n-2 and at most n-1, respectively.
EXAMPLE
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Max Alekseyev, Jun 28 2023
STATUS
approved