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

0,6

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

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 (* Jean-François Alcover, Aug 07 2018 *)

Crossrefs

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

Cf. A000041, A092080.

Sequence in context: A306727 A324209 A228107 * A104763 A027751 A378180

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