OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..90
R. K. Guy, Parker's permutation problem involves the Catalan numbers, Amer. Math. Monthly 100 (1993), 287-289.
FORMULA
a(n) = coefficient of q^((m^2-1)/2) = q(2*n*(n+1)) in the q-binomial coefficient [2*m, m] = [2*(2*n+1), 2*n+1], where m = 2*n+1. [Corrected by Petros Hadjicostas, May 30 2020]
a(n) is the number of partitions of 2*n*(n+1) into at most 2*n+1 parts each no bigger than 2*n+1. - Petros Hadjicostas, May 30 2020
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i
<n, 0, b(n, i-1, t)+b(n-i, min(i, n-i), t-1)))
end:
a:= n-> b(2*n*(n+1), 2*n+1$2):
seq(a(n), n=0..20); # Alois P. Heinz, May 30 2020
MATHEMATICA
a[n_] := SeriesCoefficient[QBinomial[2(2n+1), 2n+1, q], {q, 0, 2n(n+1)}];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Aug 19 2019 *)
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
EXTENSIONS
a(18)-a(20) from Alois P. Heinz, May 30 2020
STATUS
approved