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Search: id:A111672
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| A111672 |
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Triangle, antidiagonals are number of N-level labeled rooted trees with n leaves. |
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| 1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 12, 15, 1, 1, 5, 22, 60, 52, 1, 1, 6, 35, 154, 358, 203, 1, 1, 7, 51, 315, 1304, 2471, 877, 1, 1, 8, 70, 561, 3455, 12915, 19302, 21147, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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N-th row of the array generated from the Stirling number of the second kind triangle = the entry associated with "Number of N-level labeled rooted trees with n leaves". First few rows of the array are: 1, 1, 1, 1, 1, 1,... 1, 2, 5, 15, 52, 203,... 1, 3, 12, 60, 358, 2471,... 1, 4, 22, 154, 1304, 12915,... 1, 5, 35, 315, 3455, 44590,... 1, 6, 51, 561, 7556, 120196,... 1, 7, 70, 910, 14532, 274778,...
The rows (prefaced with another "1") are: row 2, A000110; row 3, A000258; row 4, A000307, row 5, A000357; row 6, A000405; row 7, A001669, row 8, A081624...; and so on. By columns of the triangle A111672, column 3 (1, 5, 12, 22, 35...) = A000326, column 4 = A005945.
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FORMULA
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Let the Stirling number of the second kind triangle A008277 be an infinite lower triangular matrix M. Perform M^n * [1, 0, 0, 0...] getting an array. The antidiagonals of the array become the rows of A111672; while rows of the array become diagonals of A111672.
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EXAMPLE
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Terms 1, 3, 5, 1 of an antidiagonal in the array becomes row 4 of the triangle.
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CROSSREFS
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Cf. A008277, A000326, A005945, A000110, A000258, A000307, A000357, A000405, A111669, A081624.
Sequence in context: A094954 A083064 A112338 this_sequence A128198 A123349 A123352
Adjacent sequences: A111669 A111670 A111671 this_sequence A111673 A111674 A111675
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2005
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