A370197 a(n) is the number of ways to place n indistinguishable balls into n distinguishable boxes with at least 4 boxes remaining empty.

0, 0, 0, 0, 5, 81, 658, 3830, 18525, 80587, 330330, 1312015, 5132075, 19946915, 77383374, 300272554, 1166405717, 4536991655, 17671814690, 68922126879, 269127380699, 1052047384687, 4116712577510, 16123798186665, 63205298480275, 247959260395901, 973469705104278

Offset

1,5

Comments

a(n) is also the number of weak compositions of n into n parts in which at least four parts are zero.

Links

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

Formula

a(n) = binomial(2*n-1,n) - binomial(n,2)*binomial(n-1,2) - binomial(n,3)*binomial(n-1,3) - n*(n-1) - 1.

Example

a(6)=81 since 6 can be written as 6+0+0+0+0+0, 0+6+0+0+0+0, etc. (6 such compositions); 5+1+0+0+0+0 (30 such compositions); 4+2+0+0+0+0 (30 such compositions); 3+3+0+0+0+0 (15 such compositions).

Crossrefs

Cf. A001700, A010763, A352027, A371003.

Sequence in context: A275091 A275347 A110257 * A335177 A135918 A115032

Adjacent sequences: A370194 A370195 A370196 * A370198 A370199 A370200

Keyword

nonn

Author

Enrique Navarrete, Mar 09 2024

Status

approved