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 A087648 #23 Sep 08 2022 08:45:11
%S A087648 1,3,9,31,120,514,2407,12205,66491,386699,2388096,15589732,107165081,
%T A087648 773106715,5836100685,45981026703,377230766908,3215977070706,
%U A087648 28437411817135,260380616093533,2464930698184351,24091925888687459,242802079705721156,2520198597834860148
%N A087648 a(n) = (1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)).
%C A087648 Sum of last number in all set partitions of n+1. E.g. The set partitions of 3 are {1,1,1}, {1,1,2}, {1,2,1}, {1,2,2} and {1,2,3}, so a(2) = 1+2+1+2+3 = 9. - _Franklin T. Adams-Watters_, Jun 07 2006
%C A087648 Number of partitions of the (n+2)-multiset {0,0,1,2,...,n} into distinct multisets. Also number of factorizations of 2 * Product_{i=1..n+1} prime(i) into distinct factors. - _Alois P. Heinz_, Jul 30 2021
%H A087648 Vincenzo Librandi, <a href="/A087648/b087648.txt">Table of n, a(n) for n = 0..200</a>
%t A087648 f[0]=1; f[n_] := Sum[ StirlingS2[n, k]*Binomial[k+2, k ], {k, 1, n}]; Table[ f[n], {n, 0, 20}] (* _Zerinvary Lajos_, Mar 31 2007 *)
%t A087648 (#[[3]]+#[[2]]-#[[1]])/2&/@Partition[BellB[Range[0,30]],3,1] (* _Harvey P. Dale_, Jul 20 2021 *)
%o A087648 (Magma) [(1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)) : n in [0..30]]; // _Vincenzo Librandi_, Nov 13 2011
%Y A087648 Cf. A000110, A035098, A059606.
%Y A087648 Main diagonal of A120057, row sums of A120095.
%Y A087648 Column 1 of array in A322770.
%Y A087648 Row n=2 of A346520.
%K A087648 nonn
%O A087648 0,2
%A A087648 _Vladeta Jovovic_, Sep 23 2003