A052170 Number of directed loopless multigraphs with n arcs.

1, 1, 6, 24, 130, 688, 4211, 26840, 184153, 1328155, 10078617, 79926478, 660616432, 5671793248, 50459837996, 464139053799, 4405521306315, 43077862741114, 433275511964227, 4476516495577776, 47451864583578111, 515494036824348917, 5733423512317010811, 65226494052113260251, 758377712833720838677, 9004484581478188581057

Offset: 0

Author

Vladeta Jovovic, Jan 26 2000

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A050535, A007717, A037240, A050930, A333361.

Programs

PARI

a(n)={polcoef(G(2*n, x + O(x*x^(n))), n)} \\ Needs G from A333361. - Andrew Howroyd, Mar 16 2020

PARI

\\ faster, also needs G from A333361.
EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
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))}
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

Formula

a(n) = A333361(n, 2*n). - Andrew Howroyd, Mar 16 2020

Extensions

a(16)-a(25) from Max Alekseyev, Jun 21 2011