A197743 The number of connected components in all labeled directed graphs (with self loops allowed) on n nodes.

0, 2, 20, 600, 70048, 34265920, 69135737856, 563921434969088, 18455775305195147264, 2418183926567027902291968, 1267698967252460350153517105152, 2658483881480146168943131337243754496, 22300809002478630462447974400280680553512960

Offset: 0

Author

Geoffrey Critzer, Oct 17 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A062738, A186236.

Programs

Mathematica

a=Sum[2^(n^2)x^n/n!, {n,0,20}]; Range[0,20]! CoefficientList[Series[a Log[a], {x,0,20}], x]

PARI

seq(n)={my(g=log(sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n))); Vec(serlaplace(g*exp(g)), -(n+1))} \\ Andrew Howroyd, Nov 07 2019

Formula

E.g.f.: B(A(x)) where A(x) = log(Sum_{k=1..n} 2^(n^2)x^n/n!) and B(x)= x*exp(x).

a(n) = Sum_{k=1..n} k*A186236(n,k).

Extensions

Terms a(11) and beyond from Andrew Howroyd, Nov 07 2019