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A085483
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Triangle read by rows: S_B(n,k) = `Type B' Stirling numbers of the second kind.
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3
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2, 2, 5, 2, 15, 14, 2, 35, 84, 43, 2, 75, 350, 430, 142, 2, 155, 1260, 2795, 2130, 499, 2, 315, 4214, 15050, 19880, 10479, 1850, 2, 635, 13524, 73143, 149100, 132734, 51800, 7193, 2, 1275, 42350, 334110, 987042, 1320354, 854700, 258948, 29186, 2, 2555
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..47.
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FORMULA
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A partition of {-n, ..., -1, 1, ..., n} into nonempty subsets X_1, ..., X_r is called `symmetric' if for each i -X_i = X_j for some j. S_B(n, k) is the number of such symmetric partitions whose induced partition on {1, ..., n} involves k nonempty subsets. S_B(n, k) = S(n, k) * a(k), where S(n, k) is A008277 and a(k) is A005425.
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EXAMPLE
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S_B(2,2)=5 because the relevant partitions of {-2,-1,1,2} are: {-2|-1|1|2}, {-1,1|-2|2}, {-1|1|-2,2}, {-1,1|-2,2}, {1,-2|-1,2}.
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CROSSREFS
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Cf. A008277, A005425.
S_B(n, 1)+...+S_B(n, n) = A002872(n).
Sequence in context: A192233 A144943 A114976 * A271654 A271622 A324505
Adjacent sequences: A085480 A085481 A085482 * A085484 A085485 A085486
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KEYWORD
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nonn,tabl
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AUTHOR
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James East, Aug 15 2003
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STATUS
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approved
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