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

0,2

Links

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

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A062738, A186236.

Sequence in context: A009399 A275779 A292415 * A009182 A015207 A054941

Adjacent sequences: A197740 A197741 A197742 * A197744 A197745 A197746

Keyword

nonn

Author

Geoffrey Critzer, Oct 17 2011

Extensions

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

Status

approved