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%I #23 Mar 12 2024 18:59:24
%S 0,0,0,0,5,81,658,3830,18525,80587,330330,1312015,5132075,19946915,
%T 77383374,300272554,1166405717,4536991655,17671814690,68922126879,
%U 269127380699,1052047384687,4116712577510,16123798186665,63205298480275,247959260395901,973469705104278
%N a(n) is the number of ways to place n indistinguishable balls into n distinguishable boxes with at least 4 boxes remaining empty.
%C a(n) is also the number of weak compositions of n into n parts in which at least four parts are zero.
%F 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.
%e 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).
%Y Cf. A001700, A010763, A352027, A371003.
%K nonn
%O 1,5
%A _Enrique Navarrete_, Mar 09 2024
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