%I #6 Jan 20 2024 16:24:56
%S 0,18,100,425,1666,6370,24228,92277,352594,1351933,5200130,20058103,
%T 77558534,300539938,1166802820,4537567325,17672631538,68923264009,
%U 269128936778,1052049481375,4116715363270,16123801840973,63205303218250,247959266473375,973469712823326
%N a(n) = binomial(2*n-1,n) - n^2 - 1.
%C a(n) is the number of ways to place n indistinguishable balls into n distinguishable boxes with at least 2 boxes remaining empty and not all balls placed in one box.
%t Table[Binomial[2*n - 1, n] - n^2 - 1, {n, 3, 30}] (* _Wesley Ivan Hurt_, Jan 20 2024 *)
%Y Cf. A352027.
%K nonn,easy
%O 3,2
%A _Enrique Navarrete_, Dec 31 2022