A275216 Triangle read by rows, coefficients of the q-binomials (Gaussian binomial coefficients).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 2, 1, 1, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1, 1, 1, 2, 2, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,23

Links

Seiichi Manyama, Rows n = 0..21, flattened

NIST Digital Library of Mathematical Functions, Binomial Coefficients. (Release 1.0.11 of 2016-06-08)

Index entries related to Gaussian binomial coefficients.

Example

Row 8:
{1},
{1,1,1,1,1,1,1,1},
{1,1,2,2,3,3,4,3,3,2,2,1,1},
{1,1,2,3,4,5,6,6,6,6,5,4,3,2,1,1},
{1,1,2,3,5,5,7,7,8,7,7,5,5,3,2,1,1},
{1,1,2,3,4,5,6,6,6,6,5,4,3,2,1,1},
{1,1,2,2,3,3,4,3,3,2,2,1,1},
{1,1,1,1,1,1,1,1},
{1}.

Mathematica

QPascalRow[n_] := Table[CoefficientList[QBinomial[n, k, q] // FunctionExpand, q], {k, 0, n}]; Table[QPascalRow[n], {n, 0, 7}] // Flatten

Crossrefs

See the link to the index.

Cf. A007318, A083906.

Sequence in context: A367931 A365297 A270419 * A062379 A325625 A043288

Adjacent sequences: A275213 A275214 A275215 * A275217 A275218 A275219

Keyword

nonn,look,tabf

Author

Peter Luschny, Jul 23 2016

Status

approved