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A256589
Triangle read by rows: T(n,k) divided by (n-k+1)! is the expected value of number of possible subsets in a partition of a set of n elements with no subsets of cardinality smaller than k.
1
1, 3, 1, 11, 2, 1, 50, 8, 2, 1, 274, 36, 6, 2, 1, 1764, 200, 30, 6, 2, 1, 13068, 1300, 168, 24, 6, 2, 1, 109584, 9720, 1080, 144, 24, 6, 2, 1, 1026576, 82180, 8100, 960, 120, 24, 6, 2, 1
OFFSET
1,2
COMMENTS
This sequence can be seen as a generalization of A233744 which is the particular case where minimum subset cardinality is 2 (k=2).
T(n,k) / A004736(n,k)! = 1 + 1 / ( A002024(n,k) - A002260(n,k) + 1) * (Sum of (T(n,p) / A004736(n,p)!) for p starting at A002260(n,k) up to A002024(n) - A002260(n) if 2 * A002260(n) <= A002024(n)).
The triangle below but including the diagonal is A166350 because there is only one possible partition of subsets of cardinality >= k in any set whose cardinality is between k and 2*k-1.
LINKS
EXAMPLE
The triangle T(n, k) starts:
n\k 1 2 3 4 5 6 ...
1: 1
2: 3 1
3: 11 2 1
4: 50 8 2 1
5: 274 36 6 2 1
6:1764 200 36 6 2 1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Martin Y. Champel, Apr 03 2015
STATUS
approved