OFFSET
0,6
COMMENTS
LINKS
G. C. Greubel, Rows n = 0..30 of triangle, flattened
NIST Digital Library of Mathematical Functions, q-Factorials. (Release 1.0.11 of 2016-06-08)
FORMULA
a(n) = A008302(n) for all n > 0. - M. F. Hasler, Jan 06 2024
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())
(Magma)
B:= func< n, x | n eq 0 select 1 else (&*[1-x^j: j in [1..n]])/(1-x)^n >;
R<x>:=PowerSeriesRing(Integers(), 30);
[Coefficients(R!( B(n, x) )): n in [0..9]]; // G. C. Greubel, May 22 2019
(PARI) for(n=0, 8, print1(Vec(if(n==0, 1, prod(j=1, n, 1-x^j)/(1-x)^n)), ", "); print(); ) \\ G. C. Greubel, May 23 2019
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jul 19 2016
STATUS
approved