%I A059022
%S A059022 1,1,1,1,10,1,35,1,91,1,210,280,1,456,2100,1,957,10395,1,1969,42735,
%T A059022 15400,1,4004,158301,200200,1,8086,549549,1611610,1,16263,1827826,
%U A059022 10335325,1401400,1,32631,5903898,57962905,28028000,1,65382,18682014
%N A059022 Triangle of Stirling numbers of order 3.
%C A059022 The number of partitions of the set N, |N|=n, into k blocks, all of cardinality 
               greater than or equal to 3. This is the 3-associated Stirling number 
               of the second kind (Comtet) or the Stirling number of order 3 (Fekete).
%C A059022 This is entered as a triangular array. The entries S_3(n,k) are zero 
               for 3k>n, so these values are omitted. Initial entry in sequence 
               is S_3(3,1).
%C A059022 Rows are of lengths 1,1,1,2,2,2,3,3,3,...
%D A059022 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 222.
%D A059022 A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 
               (1994), 771-778.
%D A059022 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               76.
%F A059022 S_r(n+1, k)=k S_r(n, k)+binomial(n, r-1)S_r(n-r+1, k-1) for this sequence, 
               r=3 G.f.: sum(S_r(n, k)u^k ((t^n)/(n!)), n=0..infty, k=0..infty)=exp(u(e^t-sum(t^i/
               i!, i=0..r-1)))
%e A059022 There are 10 ways of partitioning a set N of cardinality 6 into 2 blocks 
               each of cardinality at least 3, so S_3(6,2)=10.
%Y A059022 Cf. A008299, A059023, A059024, A059025.
%Y A059022 Sequence in context: A050999 A070246 A085044 this_sequence A115097 A050313 
               A116574
%Y A059022 Adjacent sequences: A059019 A059020 A059021 this_sequence A059023 A059024 
               A059025
%K A059022 nonn,tabf,nice
%O A059022 3,5
%A A059022 Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000