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%I #12 Aug 01 2016 05:51:59
%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,2,2,2,1,1,1,1,3,3,4,3,
%T 3,1,1,1,1,2,2,2,1,1,1,1,1,1,2,2,3,2,2,1,1,1,1,3,4,6,6,8,6,6,4,3,1,1,
%U 1,1,3,4,6,6,8,6,6,4,3,1,1,1,1,2,2,3,2,2,1,1,1
%N Triangle read by rows, coefficients of the q-Narayana numbers.
%e Triangle starts:
%e 1: [{1}]
%e 2: [{1}, {1}]
%e 3: [{1}, {1,1,1}, {1}]
%e 4: [{1}, {1,1,2,1,1}, {1,1,2,1,1}, {1}]
%e 5: [{1}, {1,1,2,2,2,1,1}, {1,1,3,3,4,3,3,1,1}, {1,1,2,2,2,1,1}, {1}]
%e 6: [{1}, {1,1,2,2,3,2,2,1,1}, {1,1,3,4,6,6,8,6,6,4,3,1,1},{1,1,3,4,6,6,8,6,6,4,3,1,1}, {1,1,2,2,3,2,2,1,1}, {1}]
%e Summing the {}-brackets gives the Narayana numbers, summing the []-brackets gives the Catalan numbers.
%t QNarayana[n_,k_] := QBinomial[n, k, q] QBinomial[n-1, k, q]/QBinomial[k+1,1,q];
%t QNarayanaRow[n_] := Table[CoefficientList[QNarayana[n,k] // FunctionExpand,q], {k,0,n-1}] // Flatten; Table[QNarayanaRow[n],{n,1,6}] // Flatten
%Y Cf. A000108, A001263, A275214.
%K nonn,tabf
%O 1,12
%A _Peter Luschny_, Jul 22 2016
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