%I A122420
%S A122420 1,0,1,10,120,1778,31685,661940,15882128,430607370,13022755068,
%T A122420 434697574538,15875944361864,629756003982336,26963278837704185,
%U A122420 1239382820431888898,60875147436141987437,3181961834442383306068
%N A122420 Number of labeled directed multigraphs with n arcs and with no vertex 
               of indegree 0.
%F A122420 a(n) = (1/n!)*Sum_{k=0..n} |Stirling1(n,k)|*A122418(k). G.f.: A(x/(1-x)) 
               where A(x) is g.f. for A122419.
%p A122420 A122418 := proc(n) option remember ; add( combinat[stirling2](n,k)*(k-1)^n*k!,
               k=0..n) ; end: A122420 := proc(n) option remember ; add( abs(combinat[stirling1](n,
               k))*A122418(k),k=0..n)/n! ; end: for n from 0 to 30 do printf("%d, 
               ",A122420(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               May 18 2007
%Y A122420 Cf. A104209.
%Y A122420 Sequence in context: A027568 A034255 A051582 this_sequence A069671 A138445 
               A138496
%Y A122420 Adjacent sequences: A122417 A122418 A122419 this_sequence A122421 A122422 
               A122423
%K A122420 easy,nonn
%O A122420 0,4
%A A122420 Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 03 2006
%E A122420 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007