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Search: id:A111579
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| A111579 |
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Generalized Bell number triangle, read by rows. |
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+0
3
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| 1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 8, 5, 2, 1, 1, 16, 15, 6, 2, 1, 1, 32, 52, 24, 7, 2, 1, 1, 64, 203, 116, 35, 8, 2, 1, 1, 128, 877, 648, 214, 48, 9, 2, 1, 1, 256, 4140, 4088, 1523, 352, 63, 10, 2, 1, 1, 512, 21147, 28640, 12349, 3008, 536, 80, 11, 2, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Generalized Stirling number of the second kind triangles may be defined by the generating operation T(n,k) = T(n-1,k-1) + Q*T(n-1,k) where Q denotes an arithmetic sequence (1,1,1...Pascal's triangle); (1,2,3...Stirling number of the second kind triangle); (1,3,5...A039755 an analogue of the Stirling number of the second kind triangle); etc...
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FORMULA
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Columns are row sums of generalized Stirling number of the second kind triangles.
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EXAMPLE
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Column 2 (1, 2, 5, 15, 52, 203...are Bell numbers deleting the first 1); which are row sums of the Stirling number of the second kind triangle A008277.
Column 3 (1, 2, 6, 24, 116...) = row sums of A039755, a Stirling number of the second kind analogue.
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CROSSREFS
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Cf. A008277, A000110, A039755, A004211, A111577, A111578.
Adjacent sequences: A111576 A111577 A111578 this_sequence A111580 A111581 A111582
Sequence in context: A141020 A057728 A098050 this_sequence A144018 A122773 A029268
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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 07 2005
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