

A140207


Triangle read by rows in which row n (n>=0) gives the first n terms of A000041.


9



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

0,6


COMMENTS

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 sections of n+1, where j = nk+1 (cf. A182703).  Omar E. Pol, Feb 07 2012


LINKS

Robert Price, Table of n, a(n) for n = 0..1325 (first 50 rows)
Francesca Aicardi, Matricial formulas for partitions, arXiv:0806.1273 [math.NT], 2008. [Note that there is an error in the triangle given there.]


EXAMPLE

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


MATHEMATICA

Table[PartitionsP[k], {n, 0, 12}, {k, 0, n}] // Flatten (* JeanFrançois Alcover, Aug 07 2018 *)


CROSSREFS

Mirror of triangle A027293.  Omar E. Pol, Feb 07 2012
Sequence in context: A306727 A324209 A228107 * A104763 A027751 A181322
Adjacent sequences: A140204 A140205 A140206 * A140208 A140209 A140210


KEYWORD

nonn,tabl


AUTHOR

N. J. A. Sloane, Jun 10 2008, based on a suggestion from Gary W. Adamson


STATUS

approved



