This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352405 #11 Apr 11 2022 22:01:22 %S A352405 0,2,9,30,80,180,357,644,1080,1710,2585,3762,5304,7280,9765,12840, %T A352405 16592,21114,26505,32870,40320,48972,58949,70380,83400,98150,114777, %U A352405 133434,154280,177480,203205,231632,262944,297330,334985,376110,420912,469604,522405,579540,641240,707742,779289,856130 %N A352405 a(n) = binomial(n,2)*(binomial(n-1,2) + 2). %C A352405 a(n) is the number of ways to place n indistinguishable balls into n distinguishable boxes with either 1 or 2 boxes remaining empty. %C A352405 a(n) is also the number of weak compositions of n into n parts that contain either one or two 0's. %C A352405 a(n)+1 is the number of ways to place n indistinguishable balls into n distinguishable boxes with at most 2 boxes remaining empty (just add the case of no empty boxes in which we place exactly one ball in one box). %H A352405 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A352405 G.f.: x^2*(2 - x + 5*x^2)/(1 - x)^5. - _Stefano Spezia_, Mar 15 2022 %e A352405 a(4)=30 since 4 can be written as 3+1+0+0, 0+3+0+1, etc. (12 such compositions); 2+2+0+0 (6 such compositions); 2+1+1+0 (12 such compositions). %t A352405 a[n_] := Binomial[n, 2] * (Binomial[n - 1, 2] + 2); Array[a, 50] (* _Amiram Eldar_, Mar 15 2022 *) %Y A352405 Cf. A010763, A350653. %K A352405 nonn,easy %O A352405 1,2 %A A352405 _Enrique Navarrete_, Mar 14 2022