A275215 Triangle read by rows, coefficients of the q-Narayana numbers.

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

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 A352080 A295632

Adjacent sequences: A275212 A275213 A275214 * A275216 A275217 A275218

Keyword

nonn,tabf

Author

Peter Luschny, Jul 22 2016

Status

approved