Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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