%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 = nk+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 (* _JeanFrançois 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_
