A362967 Number of nondecreasing partitions of n^2 into n parts from the intervals [1,n], [2,n+1], ..., [n,2n-1], respectively.

1, 1, 2, 5, 17, 66, 294, 1393, 6965, 36111, 192850, 1053894, 5871306, 33234990, 190704140, 1107086841, 6492325565, 38412063755, 229052915708, 1375396927729, 8310509070747, 50496841617102, 308394124109340, 1892137615326526, 11658149626059204, 72108088307308032, 447590893613564372

Offset: 0

Author

Max Alekseyev, Jun 16 2023

Keywords

• nonn

Comments

a(n) <= A039744(n); a(n) <= A077045(n); a(n) >= A019589(n).

Links

• Max Alekseyev, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A019589, A039744, A077045.

Programs

Sage

def a362967(n): return Partitions(n^2, length=n, inner=range(n,0,-1), outer=range(2*n-1,n-1,-1)).cardinality()