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E.g.f.: 1-1/B(x) where B(x) is e.g.f. for A003024.
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%I #13 Jan 24 2020 15:36:02

%S 0,1,1,13,373,24061,3430021,1085594413,765444156373,1199327541421981,

%T 4150826776751106181,31511604323119334675053,

%U 521181162682913685911315413,18663030289006900328937074926621

%N E.g.f.: 1-1/B(x) where B(x) is e.g.f. for A003024.

%D R. W. Robinson, Counting labeled acyclic digraphs, p. 264 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973

%H Andrew Howroyd, <a href="/A082403/b082403.txt">Table of n, a(n) for n = 0..50</a>

%t m = 20; b[0] = b[1] = 1;

%t b[n_] := b[n] = Sum[-(-1)^k Binomial[n, k] 2^(k (n-k)) b[n-k], {k, 1, n}];

%t B[x_] = Sum[b[n] x^n/n!, {n, 0, m}];

%t CoefficientList[1 - 1/B[x] + O[x]^(m+1), x] Range[0, m]! (* _Jean-François Alcover_, Jan 24 2020 *)

%o (PARI) \\ here G(n) gives A003024 as e.g.f.

%o G(n)={my(v=vector(n+1)); v[1]=1; for(n=1, n, v[n+1]=sum(k=1, n, -(-1)^k*2^(k*(n-k))*v[n-k+1]/k!))/n!; Ser(v)}

%o { concat([0], Vec(serlaplace(1-1/G(15)))) } \\ _Andrew Howroyd_, Sep 10 2018

%Y Cf. A003024.

%K nonn

%O 0,4

%A _Vladeta Jovovic_, Apr 15 2003