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Search: id:A133399
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| A133399 |
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Triangle T(n,k)=number of forests of labeled rooted trees with n nodes, containing exactly k trees of height one, all others having height zero (n>=0, 0<=k<=floor(n/2)). |
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3
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| 1, 1, 1, 2, 1, 9, 1, 28, 12, 1, 75, 120, 1, 186, 750, 120, 1, 441, 3780, 2100, 1, 1016, 16856, 21840, 1680, 1, 2295, 69552, 176400, 45360, 1, 5110, 272250, 1224720, 705600, 30240, 1, 11253, 1026300, 7692300, 8316000, 1164240, 1, 24564, 3762132
(list; table; graph; listen)
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OFFSET
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0,4
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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, Table of n, a(n) for n = 0..675
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FORMULA
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T(n,k)=binomial(n,k)*k!*stirling2(n-k+1,k+1).
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EXAMPLE
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Triangle begins:
1
1
1 2
1 9
1 28 12
1 75 120
1 186 750 120
1 441 3780 2100
1 1016 16856 21840 1680
1 2295 69552 176400 45360
1 5110 272250 1224720 705600 30240
...
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MAPLE
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with(combinat, stirling2); T := (n, k)->binomial (n, k)*k!*stirling2 (n-k+1, k+1); for n from 0 to 10 do lprint(seq(T(n, k), k=0..floor(n/2))) od;
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CROSSREFS
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Cf. A058877, A000248, A133386.
Sequence in context: A011186 A078088 A100945 this_sequence A128751 A129168 A024578
Adjacent sequences: A133396 A133397 A133398 this_sequence A133400 A133401 A133402
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 24 2007
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