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Search: id:A059023
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| A059023 |
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Triangle of Stirling numbers of order 4. |
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+0
5
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| 1, 1, 1, 1, 1, 35, 1, 126, 1, 336, 1, 792, 1, 1749, 5775, 1, 3718, 45045, 1, 7722, 231231, 1, 15808, 981981, 1, 32071, 3741738, 2627625, 1, 64702, 13307294, 35735700, 1, 130084, 45172842, 300179880, 1, 260984, 148417854, 2002016016, 1, 522937
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OFFSET
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4,6
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COMMENT
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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.
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).
Rows are of lengths 1,1,1,1,2,2,2,2,3,3,3,3,...
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 222.
A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 76.
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FORMULA
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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)))
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EXAMPLE
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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.
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CROSSREFS
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Cf. A008299, A059022, A059024, A059025.
Sequence in context: A067156 A104785 A028847 this_sequence A037934 A013548 A034086
Adjacent sequences: A059020 A059021 A059022 this_sequence A059024 A059025 A059026
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
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