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

1,3

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.

Links

Table of n, a(n) for n=1..27.

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.

Example

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.

Sequence in context: A055281 A346174 A182349 * A215225 A056385 A266945

Adjacent sequences: A371033 A371034 A371035 * A371037 A371038 A371039

Keyword

nonn

Author

Enrique Navarrete, Mar 08 2024

Status

approved