This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256589 #44 Jul 27 2024 02:35:26 %S A256589 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 A256589 24,6,2,1,109584,9720,1080,144,24,6,2,1,1026576,82180,8100,960,120,24, %U A256589 6,2,1 %N 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. %C A256589 This sequence can be seen as a generalization of A233744 which is the particular case where minimum subset cardinality is 2 (k=2). %C A256589 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 A256589 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 A256589 Martin Y. Champel, <a href="/A256589/b256589.txt">Table of n, a(n) for n = 1..10000</a> %e A256589 The triangle T(n, k) starts: %e A256589 n\k 1 2 3 4 5 6 ... %e A256589 1: 1 %e A256589 2: 3 1 %e A256589 3: 11 2 1 %e A256589 4: 50 8 2 1 %e A256589 5: 274 36 6 2 1 %e A256589 6:1764 200 36 6 2 1 %Y A256589 Column 2 is A233744. %Y A256589 Cf. A002024, A002260, A004736, A026791, A166350, A135010. %K A256589 nonn,tabl %O A256589 1,2 %A A256589 _Martin Y. Champel_, Apr 03 2015