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A059025
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Triangle of Stirling numbers of order 6.
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4
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1, 1, 1, 1, 1, 1, 1, 462, 1, 1716, 1, 4719, 1, 11440, 1, 25883, 1, 56134, 1, 118456, 2858856, 1, 245480, 23279256, 1, 502588, 124710300, 1, 1020680, 551496660, 1, 2061709, 2181183147, 1, 4149752, 8021782197, 1, 8333153, 28051272535
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,8
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COMMENTS
| The number of partitions of the set N, |N|=n, into k blocks, all of cardinality greater than or equal to 6. This is the 6-associated Stirling number of the second kind.
This is entered as a triangular array. The entries S_6(n,k) are zero for 6k>n, so these values are omitted. Initial entry in sequence is S_6(6,1).
Rows are of lengths 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, ...
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REFERENCES
| 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
| 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=6 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
| There are 462 ways of partitioning a set N of cardinality 12 into 2 blocks each of cardinality at least 6, so S_6(12,2)=462.
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CROSSREFS
| Cf. A008299, A059022, A059023, A059024.
Sequence in context: A138956 A107121 A101734 * A094380 A104397 A108749
Adjacent sequences: A059022 A059023 A059024 * A059026 A059027 A059028
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KEYWORD
| nonn,tabf,nice
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AUTHOR
| Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000 # Extensions to existing sequences
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