OFFSET
0,9
COMMENTS
The Bell transform of g(n) = 1 if n<6 else 0. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 19 2016
LINKS
Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394, 2017.
David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009 (see Table 7 E5(n,k) page 16).
FORMULA
Bivariate e.g.f. A151511(x,t) = Sum_{n>=0, k>=0} T(n,k)*x^n*t^k/n! = exp(t*G6(x)), where G6(x) = Sum_{i=1..6} x^i/i! is the e.g.f. of column 1. - R. J. Mathar, May 28 2019
EXAMPLE
Triangle begins:
1
0 1
0 1 1
0 1 3 1
0 1 7 6 1
0 1 15 25 10 1
0 1 31 90 65 15 1
0 0 63 301 350 140 21 1
0 0 119 966 1701 1050 266 28 1
MATHEMATICA
Unprotect[Power]; 0^0 = 1; a[n_ /; 1 <= n <= 6] = 1; a[_] = 0; T[n_, k_] := T[n, k] = If[k == 0, a[0]^n, Sum[Binomial[n - 1, j - 1] a[j] T[n - j, k - 1], {j, 0, n - k + 1}]]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 20 2016, after Peter Luschny *)
PROG
(Sage) # uses[bell_matrix from A264428]
bell_matrix(lambda n: 1 if n<6 else 0, 12) # Peter Luschny, Jan 19 2016
CROSSREFS
Begins in same way as triangle of Stirling numbers of second kind, A048993, but is strictly different. N. J. A. Sloane, Aug 09 2017
KEYWORD
AUTHOR
N. J. A. Sloane, May 14 2009
EXTENSIONS
Row 9 added by Michel Marcus, Feb 13 2014
More rows from R. J. Mathar, May 28 2019
STATUS
approved