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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A232744 can be found in the second column of this triangle. 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 Martin Y. Champel, Table of n, a(n) for n = 1..10000 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 Cf. A002024, A002260, A004736, A026791, A166350, A135010, A233744. Sequence in context: A205483 A230262 A323854 * A229834 A120291 A099001 Adjacent sequences: A256586 A256587 A256588 * A256590 A256591 A256592 KEYWORD nonn,tabl AUTHOR Martin Y. Champel, Apr 03 2015 STATUS approved

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Last modified October 3 22:39 EDT 2023. Contains 365872 sequences. (Running on oeis4.)