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Search: id:A059024
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| A059024 |
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Triangle of Stirling numbers of order 5. |
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+0
5
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| 1, 1, 1, 1, 1, 1, 126, 1, 462, 1, 1254, 1, 3003, 1, 6721, 1, 14443, 126126, 1, 30251, 1009008, 1, 62322, 5309304, 1, 127024, 23075052, 1, 257108, 89791416, 1, 518092, 325355316, 488864376, 1, 1041029, 1122632043, 6844101264, 1, 2088043
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OFFSET
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5,7
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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 5. This is the 5-associated Stirling number of the second kind.
This is entered as a triangular array. The entries S_5(n,k) are zero for 5k>n, so these values are omitted. Initial entry in sequence is S_5(5,1).
Rows are of lengths 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,...
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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=5 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 126 ways of partitioning a set N of cardinality 10 into 2 blocks each of cardinality at least 5, so S_5(10,2)=126.
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CROSSREFS
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Cf. A008299, A059022, A059023, A059025.
Sequence in context: A048563 A110825 A050451 this_sequence A100730 A044876 A080539
Adjacent sequences: A059021 A059022 A059023 this_sequence A059025 A059026 A059027
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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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