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A274882 a(n) is the largest coefficient of q-binomial(2*n, n) / q-binomial(n+1, 1), which are the q-Catalan polynomials. 1
1, 1, 1, 1, 2, 4, 9, 23, 62, 176, 512, 1551, 4822, 15266, 49141, 160728, 532890, 1785162, 6039328, 20617808, 70951548, 245911020, 857888714, 3010811846, 10624583264, 37680980256, 134260382400, 480440869030, 1726092837412, 6224442777366, 22523780202156 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..30.

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).subs(q=SR.var('x')).list()

print [max(T(n)) for n in (0..10)]

CROSSREFS

Cf. A000108, A129175 (coefficients of q_Catalan polynomials), A275213.

Sequence in context: A032010 A032028 A190277 * A127384 A058585 A001573

Adjacent sequences:  A274879 A274880 A274881 * A274883 A274884 A274885

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 19 2016

STATUS

approved

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Last modified May 21 17:27 EDT 2019. Contains 323444 sequences. (Running on oeis4.)