%I A059023
%S A059023 1,1,1,1,1,35,1,126,1,336,1,792,1,1749,5775,1,3718,45045,1,7722,231231,
%T A059023 1,15808,981981,1,32071,3741738,2627625,1,64702,13307294,35735700,1,
%U A059023 130084,45172842,300179880,1,260984,148417854,2002016016,1,522937
%N A059023 Triangle of Stirling numbers of order 4.
%C A059023 The number of partitions of the set N, |N|=n, into k blocks, all of cardinality 
               greater than or equal to 4. This is the 4-associated Stirling number 
               of the second kind.
%C A059023 This is entered as a triangular array. The entries S_4(n,k) are zero 
               for 4k>n, so these values are omitted. Initial entry in sequence 
               is S_4(4,1).
%C A059023 Rows are of lengths 1,1,1,1,2,2,2,2,3,3,3,3,...
%D A059023 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 222.
%D A059023 A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 
               (1994), 771-778.
%D A059023 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               76.
%F A059023 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=4 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 A059023 There are 35 ways of partitioning a set N of cardinality 8 into 2 blocks 
               each of cardinality at least 4, so S_4(8,2)=35.
%Y A059023 Cf. A008299, A059022, A059024, A059025.
%Y A059023 Sequence in context: A067156 A104785 A028847 this_sequence A037934 A013548 
               A034086
%Y A059023 Adjacent sequences: A059020 A059021 A059022 this_sequence A059024 A059025 
               A059026
%K A059023 nonn,tabf,nice
%O A059023 4,6
%A A059023 Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000