OFFSET
1,3
COMMENTS
LINKS
Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_1 Triangles.
FORMULA
T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n
T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that
1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),
f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-2}(j-n+6).
EXAMPLE
1
1 4
1 12 12
1 72 48 24
1 280 600 120 24
1 1740 4560 1800 144 0
1 8484 40740 21000 2520 0 0
1 57232 390432 223440 33600 0 0 0
1 328752 3811248 2845584 438480 0 0 0 0
1 2389140
CROSSREFS
KEYWORD
AUTHOR
Peter Luschny, Mar 07 2009, Mar 14 2009
STATUS
approved