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

Author

Enrique Navarrete, Mar 09 2024

Keywords

• nonn

Comments

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

Examples

			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.

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.