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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, 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.
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
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Mar 09 2024
STATUS
approved