login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274887 Triangle read by rows: coefficients of the q-factorial. 2
1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 6, 5, 3, 1, 1, 4, 9, 15, 20, 22, 20, 15, 9, 4, 1, 1, 5, 14, 29, 49, 71, 90, 101, 101, 90, 71, 49, 29, 14, 5, 1, 1, 6, 20, 49, 98, 169, 259, 359, 455, 531, 573, 573, 531, 455, 359, 259, 169, 98, 49, 20, 6, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

The main entry for this sequence is A008302 (Mahonian numbers).

q-factorial(n) is a univariate polynomial over the integers with degree n*(n-1)/2.

Evaluated at q=1 the q-factorial(n) gives the factorial A000142(n).

LINKS

Table of n, a(n) for n=0..63.

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

EXAMPLE

The polynomials start:

[0] 1

[1] 1

[2] q + 1

[3] (q + 1) * (q^2 + q + 1)

[4] (q + 1)^2 * (q^2 + 1) * (q^2 + q + 1)

[5] (q + 1)^2 * (q^2 + 1) * (q^2 + q + 1) * (q^4 + q^3 + q^2 + q + 1)

The triangle starts:

[1]

[1]

[1, 1]

[1, 2, 2, 1]

[1, 3, 5, 6, 5, 3, 1]

[1, 4, 9, 15, 20, 22, 20, 15, 9, 4, 1]

[1, 5, 14, 29, 49, 71, 90, 101, 101, 90, 71, 49, 29, 14, 5, 1]

MATHEMATICA

Table[CoefficientList[QFactorial[n, q] // FunctionExpand, q], {n, 0, 9}] // Flatten

PROG

(Sage)

from sage.combinat.q_analogues import q_factorial

for n in (0..5): print q_factorial(n).list()

CROSSREFS

Cf. A008302, A000142 (row sums), A063746 (q-central_binomial), A129175 (q-Catalan), A274886 (q-extended_Catalan), A274888 (q-swing_factorial), A275216 (q-binomial), A275215 (q-Narayana).

Sequence in context: A215563 A076263 A272689 * A008302 A131791 A010358

Adjacent sequences:  A274884 A274885 A274886 * A274888 A274889 A274890

KEYWORD

nonn,tabf

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 17:42 EDT 2018. Contains 316498 sequences. (Running on oeis4.)