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%I #12 Mar 16 2020 22:16:18
%S 1,1,6,24,130,688,4211,26840,184153,1328155,10078617,79926478,
%T 660616432,5671793248,50459837996,464139053799,4405521306315,
%U 43077862741114,433275511964227,4476516495577776,47451864583578111,515494036824348917,5733423512317010811,65226494052113260251,758377712833720838677,9004484581478188581057
%N Number of directed loopless multigraphs with n arcs.
%H Andrew Howroyd, <a href="/A052170/b052170.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = A333361(n, 2*n). - _Andrew Howroyd_, Mar 16 2020
%o (PARI) a(n)={polcoef(G(2*n, x + O(x*x^(n))), n)} \\ Needs G from A333361. - _Andrew Howroyd_, Mar 16 2020
%o (PARI) \\ faster, also needs G from A333361.
%o EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o InvEulerMT(u)={my(n=#u, p=log(1+x*Ser(u)), vars=variables(p)); Vec(sum(i=1, n, moebius(i)*substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i))}
%o seq(n)={concat([1], EulerT(Vec(-1 + vecsum(InvEulerMT(vector(n+1, k, G(k, y + O(y*y^n))))))))} \\ _Andrew Howroyd_, Mar 16 2020
%Y Cf. A050535, A007717, A037240, A050930, A333361.
%K nonn
%O 0,3
%A _Vladeta Jovovic_, Jan 26 2000
%E a(16)-a(25) from _Max Alekseyev_, Jun 21 2011
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