|
%I #5 May 10 2013 12:45:46
%S 1,2,1,8,18,12,1,18,108,272,300,120,1,33,393,2102,5700,8160,5880,1680,
%T 1,54,1122,10688,53550,153132,258720,255360,136080,30240,1,82,2754,
%U 42752,351650,1688892,5025832,9540272,11566800,8668800,3659040,665280
%N Triangle T(n,k) of number of labeled directed multigraphs (with loops), without isolated vertices, with n arrows and k vertices (n = 1,2,.., k = 1..2*n).
%F T(n,k) = Sum_{j=0..k} (-1)^(k-j)*binomial(k,j)*binomial(j^2+n-1,n). Row sums give A104209.
%F E.g.f.: exp(-x)*Sum((1-y)^(-n^2)*x^n/n!,n=0..infinity). - _Vladeta Jovovic_, Aug 24 2006
%e [1,2], [1,8,18,12], [1,18,108,272,300,120], [1,33,393,2102,5700,8160,5880,1680], ....
%Y Row sums give A104209.
%K nonn,tabf
%O 1,2
%A _Vladeta Jovovic_, Aug 19 2006
|
