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Search: id:A124427
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| A124427 |
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Sum of the sizes of the blocks containing the element 1 in all set partitions of {1,2,...,n}. |
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+0
1
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| 1, 3, 9, 30, 112, 463, 2095, 10279, 54267, 306298, 1838320, 11677867, 78207601, 550277003, 4055549053, 31224520322, 250547144156, 2090779592827, 18110124715919, 162546260131455, 1509352980864191, 14478981877739094
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n)=Sum(k*binom(n-1,k-1)*B(n-k), k=1..n), where B(q) are the Bell numbers (A000110).
a(n) = (n-1)*B(n-1)+B(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 10 2006
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EXAMPLE
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a(3)=9 because the 5 (=A000110(3)) set partitions of {1,2,3} are 123, 12|3, 13|2, 1|23. and 1|2|3 and 3+2+2+1+1=9.
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MAPLE
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with(combinat): 1, seq(sum(k*binomial(n-1, k-1)*bell(n-k), k=1..n), n=2..24);
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CROSSREFS
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Cf. A000110, A056857.
Sequence in context: A107379 A117428 A134168 this_sequence A055730 A120018 A091353
Adjacent sequences: A124424 A124425 A124426 this_sequence A124428 A124429 A124430
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 10 2006
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