A115724 Number of partitions with maximum rectangle n.

1, 1, 3, 5, 16, 16, 76, 53, 218, 303, 750, 412, 3680, 1361, 5015, 9206, 23162, 8290, 66166, 19936, 161656, 192181, 236007, 100730, 1338186, 819694, 1180478, 1924986, 5215844, 1246468, 17370367, 3098322, 24926724, 23473968, 24790503, 41886304, 227243488

Offset: 0

Author

Franklin T. Adams-Watters, Mar 11 2006

Keywords

• nonn

Examples

			The 16 partitions with maximum rectangle 4 are [4], [2^2], [1^4], [4,1], [3,2], [2^2,1], [2,1^3], [4,2], [4,1^2], [3,2,1], [3,1^3], [2^2,1^2], [4,2,1], [4,1^3], [3,2,1^2] and [4,2,1^2].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100
• Eric Weisstein's World of Mathematics, Ferrers Diagram.

Crossrefs

Cf. A115725, A115723, A115726, A115727.

Formula

a(n) = A115725(n) - A115725(n-1).