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A275215 Triangle read by rows, coefficients of the q-Narayana numbers. 2
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, 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, 1, 1, 3, 4, 6, 6, 8, 6, 6, 4, 3, 1, 1, 1, 1, 2, 2, 3, 2, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..91.

EXAMPLE

Triangle starts:

1: [{1}]

2: [{1}, {1}]

3: [{1}, {1,1,1}, {1}]

4: [{1}, {1,1,2,1,1}, {1,1,2,1,1}, {1}]

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}]

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}]

Summing the {}-brackets gives the Narayana numbers, summing the []-brackets gives the Catalan numbers.

MATHEMATICA

QNarayana[n_, k_] := QBinomial[n, k, q] QBinomial[n-1, k, q]/QBinomial[k+1, 1, q];

QNarayanaRow[n_] := Table[CoefficientList[QNarayana[n, k] // FunctionExpand, q], {k, 0, n-1}] // Flatten; Table[QNarayanaRow[n], {n, 1, 6}] // Flatten

CROSSREFS

Cf. A000108, A001263, A275214.

Sequence in context: A249545 A296081 A074064 * A304886 A295632 A139549

Adjacent sequences:  A275212 A275213 A275214 * A275216 A275217 A275218

KEYWORD

nonn,tabf

AUTHOR

Peter Luschny, Jul 22 2016

STATUS

approved

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Last modified May 19 16:51 EDT 2019. Contains 323395 sequences. (Running on oeis4.)