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Search: id:A124325
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| A124325 |
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Number of blocks of size >1 in all partitions of an n-set. |
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+0
2
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| 0, 0, 1, 4, 17, 76, 362, 1842, 9991, 57568, 351125, 2259302, 15288000, 108478124, 805037105, 6233693772, 50257390937, 421049519856, 3659097742426, 32931956713294, 306490813820239, 2945638599347760, 29198154161188501
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n)=Sum(k*A123324(n,k),k=0..floor(n/2)).
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FORMULA
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a(n)=B(n+1)-B(n)-nB(n-1), where B(q) are the Bell numbers (A000110). E.g.f.=[exp(z)-1-z]exp(exp(z)-1).
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EXAMPLE
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a(3)=4 because in the partitions 123, 12|3, 13|2, 1|23, 1|2|3 we have four blocks of size >1.
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MAPLE
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with(combinat): c:=n->bell(n+1)-bell(n)-n*bell(n-1): seq(c(n), n=0..23);
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CROSSREFS
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Cf. A000110, A123324.
Sequence in context: A081186 A005572 A081922 this_sequence A151248 A104455 A123952
Adjacent sequences: A124322 A124323 A124324 this_sequence A124326 A124327 A124328
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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), Oct 28 2006
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