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 A140188 #12 Jul 28 2020 11:32:00 %S A140188 1,1,1,1,1,1,2,3,1,1,1,3,3,1,1,2,4,5,3,1,1,1,5,6,5,3,1,1,5,8,10,9,5,3, %T A140188 1,1,2,10,14,12,9,5,3,1,1,2,13,21,20,15,9,5,3,1,1,1,13,24,29,23,15,9, %U A140188 5,3,1,1,5,20,39,42,37,27,15,9,5,3,1,1,1,19,43,58,53,40,27,15,9,5,3,1,1,2 %N A140188 Table read by rows: T(n,k) is the number of groupoids (categories all of whose morphisms are invertible) with n morphisms and k objects. %C A140188 The first column is T(n,1) = A000001(n) (number of groups of order n). %C A140188 T(n,k) >= A136406(n,k). %C A140188 The sum of the n^th row is A140189(n). %C A140188 For 2k<=n, T(n,n-k) = A140190(k) does not depend on n. %F A140188 T(n,k) is the sum over the quadratic bi-partitions (n_i,k_i) of (n,k) (see A136406) of the "product" of the A000001(n_i), where the "product" is the usual product except when (n_i1,k_i1)=...=(n_ip,k_ip), in which case a^p is replaced by binomial(a+p-1,p). %Y A140188 Cf. A140185. %K A140188 nonn,tabl %O A140188 1,7 %A A140188 _Benoit Jubin_, May 12 2008