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

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

Offset: 0

Author

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

Keywords

• nonn
• tabl

Comments

Number of partitions of n into distinct parts with maximal size, see A000009. - Reinhard Zumkeller, Jun 13 2009

Equals A092080 when first column is removed. Georg Fischer, Jul 26 2023

Examples

			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
		

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.]

Crossrefs

Mirror of triangle A027293. - Omar E. Pol, Feb 07 2012

Cf. A000041, A092080.

Programs

Mathematica

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