OFFSET
1,4
COMMENTS
Three-dimensional arrays don't really work in the OEIS, but this one seems like it should be included. See Good-Tideman for precise definition.
LINKS
I. J. Good, T. N. Tideman, Stirling numbers and a geometric structure from voting theory, Journal of Combinatorial Theory, Series A Volume 23, Issue 1, July 1977, Pages 34-45.
Warren D. Smith, D-dimensional orderings and Stirling numbers, October 2014.
FORMULA
There is a formula involving Stirling numbers.
EXAMPLE
The initial triangular slices are:
1
-
1
1 2
---
1
3 4
1 6 6
-----
1
6 7
7 24 18
1 14 36 24
----------
1
10 11
25 70 46
15 100 180 96
1 30 150 240 120
----------------
1
15 16
65 165 101
90 455 690 326
31 360 1170 1440 600
1 62 540 1560 1800 720
MATHEMATICA
S1[m_, n_] := Abs[StirlingS1[m, m - n]];
S2[m_, n_] := StirlingS2[m, m - n];
Nr[r_, p_, m_] := S2[m, p - r] Sum[S1[m - p + r, nu], {nu, 0, r}];
Table[Nr[r, p, m], {m, 1, 6}, {p, 0, m - 1}, {r, 0, p}] // Flatten (* Jean-François Alcover, Nov 01 2018 *)
CROSSREFS
KEYWORD
nonn,tabf,more
AUTHOR
N. J. A. Sloane, Oct 29 2014
EXTENSIONS
More terms from Michel Marcus, Aug 28 2015
STATUS
approved