The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A333142 Triangle read by rows: T(n, k) = qStirling1(n, k, q) for q = 2, with 0 <= k <= n. 2
 1, 1, 1, 1, 2, 1, 1, 7, 5, 1, 1, 50, 42, 12, 1, 1, 751, 680, 222, 27, 1, 1, 23282, 21831, 7562, 1059, 58, 1, 1, 1466767, 1398635, 498237, 74279, 4713, 121, 1, 1, 186279410, 179093412, 64674734, 9931670, 672830, 20080, 248, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS 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 T(n,n-1) = A000325(n). Cf. A333143. Sequence in context: A143670 A169730 A220725 * A196832 A005450 A039760 Adjacent sequences: A333139 A333140 A333141 * A333143 A333144 A333145 KEYWORD nonn,tabl AUTHOR Peter Luschny, Mar 09 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 06:50 EST 2022. Contains 358362 sequences. (Running on oeis4.)