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Search: id:A133386
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| A133386 |
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Number of forests of labeled rooted trees with n nodes, containing exactly 2 trees of height one, all others having height zero. |
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+0
2
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| 0, 0, 0, 0, 12, 120, 750, 3780, 16856, 69552, 272250, 1026300, 3762132, 13498056, 47615750, 165683700, 570024240, 1942538592, 6566094450, 22038141420, 73510278380, 243854707320, 804962754750, 2645408201700, 8658857196552
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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A. P. Heinz, Finding Two-Tree-Factor Elements of Tableau-Defined Monoids in Time O(n^3), Ed. S. G. Akl, F. Fiala, W. W. Koczkodaj: Advances in Computing and Information, ICCI90 Niagara Falls, LNCS 468, Springer-Verlag (1990), pp. 120-128.
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LINKS
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 05 2007, Table of n, a(n) for n = 0..100
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FORMULA
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a(n) = n*(n-1)*stirling2(n-1,3).
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EXAMPLE
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a(4)=12 because 12 trees of the given kind exist: 1<-3 2<-4, 1<-4 2<-3, 1<-2 3<-4, 1<-4 3<-2, 1<-2 4<-3, 1<-3 4<-2, 2<-1 3<-4, 2<-4 3<-1, 2<-1 4<-3, 2<-3 4<-1, 3<-1 4<-2, and 3<-2 4<-1.
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MAPLE
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with(combinat, stirling2); a := n->n*(n-1)*stirling2(n-1, 3); seq(a(n), n=0..50);
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CROSSREFS
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Cf. A058877, A000248.
Sequence in context: A121032 A093334 A001816 this_sequence A056320 A056311 A009050
Adjacent sequences: A133383 A133384 A133385 this_sequence A133387 A133388 A133389
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 22 2007
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