This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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