A371036 a(n) is the number of ways to place n indistinguishable balls into n distinguishable boxes with at least one box remaining empty and not all balls placed in a single box.

0, 0, 6, 30, 120, 455, 1708, 6426, 24300, 92367, 352704, 1352065, 5200286, 20058285, 77558744, 300540178, 1166803092, 4537567631, 17672631880, 68923264389, 269128937198, 1052049481837, 4116715363776, 16123801841525, 63205303218850, 247959266474025, 973469712824028

Offset: 1

Author

Enrique Navarrete, Mar 08 2024

Keywords

• nonn

Comments

a(n) is also the number of weak compositions of n into n parts in which at least one part is zero and the composition does not contain a single nonzero part.

Examples

			a(4)=30 since 4 can be written as 3+1+0+0, 0+3+1+0, etc. (12 such compositions); 2+2+0+0 (6 such compositions); 2+1+1+0 (12 such compositions).
		

Crossrefs

Cf. A001700, A010763, A048775, A352027, A359435.

Formula

a(n) = binomial(2n-1,n)-n-1, n > 1; a(1)=0.

a(n) = A048775(n-1)-1, n > 1.

a(n) = A001700(n-1)-(n+1), n > 1.