OFFSET
0,5
FORMULA
qStirling1(n, k, q) = qStirling1(n-1, k-1, q) + qBrackets(n-1, q)*qStirling1(n-1, k, q) with boundary values 0^k if n = 0 and n^0 if k = 0.
Note that also a second definition is used in the literature. The two versions differ by a factor of q^(n-k).
EXAMPLE
Triangle starts:
[0] 1
[1] 1, 1
[2] 1, 2, 1
[3] 1, 7, 5, 1
[4] 1, 50, 42, 12, 1
[5] 1, 751, 680, 222, 27, 1
[6] 1, 23282, 21831, 7562, 1059, 58, 1
[7] 1, 1466767, 1398635, 498237, 74279, 4713, 121, 1
[8] 1, 186279410, 179093412, 64674734, 9931670, 672830, 20080, 248, 1
MAPLE
qStirling1 := proc(n, k, q) option remember; with(QDifferenceEquations):
if n = 0 then return 0^k fi; if k = 0 then return n^0 fi;
qStirling1(n-1, k-1, p) + QBrackets(n-1, p)*qStirling1(n-1, k, p);
subs(p = q, expand(%)) end:
seq(seq(qStirling1(n, k, 2), k=0..n), n=0..9);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 09 2020
STATUS
approved