cp's OEIS Frontend

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.

%I A371036 #11 Mar 28 2024 23:54:33
%S A371036 0,0,6,30,120,455,1708,6426,24300,92367,352704,1352065,5200286,
%T A371036 20058285,77558744,300540178,1166803092,4537567631,17672631880,
%U A371036 68923264389,269128937198,1052049481837,4116715363776,16123801841525,63205303218850,247959266474025,973469712824028
%N 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.
%C A371036 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.
%F A371036 a(n) = binomial(2n-1,n)-n-1, n > 1; a(1)=0.
%F A371036 a(n) = A048775(n-1)-1, n > 1.
%F A371036 a(n) = A001700(n-1)-(n+1), n > 1.
%e A371036 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).
%Y A371036 Cf. A001700, A010763, A048775, A352027, A359435.
%K A371036 nonn
%O A371036 1,3
%A A371036 _Enrique Navarrete_, Mar 08 2024