Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #44 Jul 27 2024 02:35:26
%S 1,3,1,11,2,1,50,8,2,1,274,36,6,2,1,1764,200,30,6,2,1,13068,1300,168,
%T 24,6,2,1,109584,9720,1080,144,24,6,2,1,1026576,82180,8100,960,120,24,
%U 6,2,1
%N 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.
%C This sequence can be seen as a generalization of A233744 which is the particular case where minimum subset cardinality is 2 (k=2).
%C 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)).
%C 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.
%H Martin Y. Champel, <a href="/A256589/b256589.txt">Table of n, a(n) for n = 1..10000</a>
%e The triangle T(n, k) starts:
%e n\k 1 2 3 4 5 6 ...
%e 1: 1
%e 2: 3 1
%e 3: 11 2 1
%e 4: 50 8 2 1
%e 5: 274 36 6 2 1
%e 6:1764 200 36 6 2 1
%Y Column 2 is A233744.
%Y Cf. A002024, A002260, A004736, A026791, A166350, A135010.
%K nonn,tabl
%O 1,2
%A _Martin Y. Champel_, Apr 03 2015