OFFSET
0,5
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..200
FORMULA
Conjecture: a(n) ~ sqrt(3) * 2^(2*n) / (Pi * n^3). - Vaclav Kotesovec, Jan 06 2023
MAPLE
with(QDifferenceEquations): MaxQCatalan := proc(n) local P; P := f -> expand(simplify(expand(f))); P(QBinomial(2*n, n, q)/QBrackets(n+1, q)); max(seq(coeff(%, q, j), j=0..degree(%))) end: seq(MaxQCatalan(n), n=0..20);
MATHEMATICA
p[n_] := QBinomial[2n, n, q]/QBinomial[n+1, 1, q]; Table[Max[CoefficientList[p[n] // FunctionExpand, q]], {n, 0, 20}] // Flatten
PROG
(Sage)
from sage.combinat.q_analogues import q_catalan_number
def T(n): return q_catalan_number(n)
print([max(T(n)) for n in (0..10)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 19 2016
STATUS
approved