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A140207 Triangle read by rows in which row n (n>=0) gives the first n terms of A000041. 9

%I

%S 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,

%T 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,

%U 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

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

%C Number of partitions of n into distinct parts with maximal size, see A000009. - _Reinhard Zumkeller_, Jun 13 2009

%C 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 = n-k+1 (cf. A182703). - _Omar E. Pol_, Feb 07 2012

%H Robert Price, <a href="/A140207/b140207.txt">Table of n, a(n) for n = 0..1325</a> (first 50 rows)

%H Francesca Aicardi, <a href="http://arxiv.org/abs/0806.1273">Matricial formulas for partitions</a>, arXiv:0806.1273 [math.NT], 2008. [Note that there is an error in the triangle given there.]

%e Triangle begins:

%e 1

%e 1,1

%e 1,1,2

%e 1,1,2,3

%e 1,1,2,3,5

%e 1,1,2,3,5,7

%e 1,1,2,3,5,7,11

%e 1,1,2,3,5,7,11,15

%e 1,1,2,3,5,7,11,15,22

%e 1,1,2,3,5,7,11,15,22,30

%e 1,1,2,3,5,7,11,15,22,30,42

%e 1,1,2,3,5,7,11,15,22,30,42,56

%e 1,1,2,3,5,7,11,15,22,30,42,56,77

%e 1,1,2,3,5,7,11,15,22,30,42,56,77,101

%t Table[PartitionsP[k], {n, 0, 12}, {k, 0, n}] // Flatten (* _Jean-Fran├žois Alcover_, Aug 07 2018 *)

%Y Mirror of triangle A027293. - _Omar E. Pol_, Feb 07 2012

%K nonn,tabl

%O 0,6

%A _N. J. A. Sloane_, Jun 10 2008, based on a suggestion from _Gary W. Adamson_

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Last modified March 5 00:01 EST 2021. Contains 341812 sequences. (Running on oeis4.)