A120380 Number of partitions of n*(n+1).

1, 2, 11, 77, 627, 5604, 53174, 526823, 5392783, 56634173, 607163746, 6620830889, 73232243759, 819876908323, 9275102575355, 105882246722733, 1218374349844333, 14118662665280005, 164637479165761044, 1930656072350465812, 22755290216580025259, 269435605212954994471

Offset: 0

Author

Zerinvary Lajos, Jun 29 2006

Keywords

• nonn

Examples

			a(2)=11 because the number of partitions of 6 is 11.
		

Links

• Henry Bottomley, Partition and composition calculator.
• G. P. Michon, Partition Function

Crossrefs

Cf. A000041, A003107, A002378.

Programs

Maple

with(combinat); [seq(numbpart(n*(n+1)),n=1..20)];
with(combinat): seq(numbpart(n*(n+1)),n=0..21);

Mathematica

Table[PartitionsP[n*(n+1)],{n,0,21}] (* James C. McMahon, Sep 30 2024 *)

PARI

a(n)=numbpart(n^2+n) /* Michael Somos, Jul 24 2006 */

Formula

a(n) = A000041(A002378(n)). - Michel Marcus, Sep 30 2024

Extensions

Edited by Michael Somos, Emeric Deutsch and N. J. A. Sloane, Jul 23 2006