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A140207
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Triangle read by rows in which row n (n>=0) gives the first n terms of A000041.
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7
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1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 5, 1, 1, 2, 3, 5, 7, 1, 1, 2, 3, 5, 7, 11, 1, 1, 2, 3, 5, 7, 11, 15, 1, 1, 2, 3, 5, 7, 11, 15, 22, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77
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OFFSET
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0,6
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COMMENTS
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Number of partitions of n into distinct parts with maximal size, see A000009. - Reinhard Zumkeller, Jun 13 2009
It appears that T(n,k) is also the total number of occurrences of j in the last j shells of n+1, where j = n-k+1 (cf. A182703). - Omar E. Pol, Feb 07 2012
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LINKS
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Table of n, a(n) for n=0..90.
Francesca Aicardi, Matricial formulas for partitions, arXiv:0806.1273. [Note that there is an error in the triangle given there.]
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EXAMPLE
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Triangle begins:
1
1,1
1,1,2
1,1,2,3
1,1,2,3,5
1,1,2,3,5,7
1,1,2,3,5,7,11
1,1,2,3,5,7,11,15
1,1,2,3,5,7,11,15,22
1,1,2,3,5,7,11,15,22,30
1,1,2,3,5,7,11,15,22,30,42
1,1,2,3,5,7,11,15,22,30,42,56
1,1,2,3,5,7,11,15,22,30,42,56,77
1,1,2,3,5,7,11,15,22,30,42,56,77,101
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MATHEMATICA
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Table[PartitionsP[k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 07 2018 *)
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CROSSREFS
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Mirror of triangle A027293. - Omar E. Pol, Feb 07 2012
Sequence in context: A144328 A128227 A228107 * A104763 A027751 A181322
Adjacent sequences: A140204 A140205 A140206 * A140208 A140209 A140210
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, Jun 10 2008, based on a suggestion from Gary W. Adamson
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STATUS
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approved
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