Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A refinement of the formula for $k$-ary trees and the
  Gould-Vandermonde's convolution
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ