A372920 Total number of n-colorings of all graphs on n labeled nodes.

1, 1, 6, 123, 7108, 1058885, 386056326, 332908216711, 662759754883080, 2991536714452469769, 30189087071961437767690, 673536638307789642838763531, 32919693104791033024939149066252, 3498056629389633452501822564131061773, 802931613320922331646386276441560583143438

Offset: 0

Author

Alois P. Heinz, May 16 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..76

Crossrefs

Main diagonal of A322280.

Cf. A000035, A006125.

Programs

Mathematica

nmax = 76;
a[n_] := 2^(n(n-1)/2)*n!*SeriesCoefficient[Sum[x^i/(2^(i(i-1)/2)*i!), {i, 0, nmax}]^n, {x, 0, n}];
Table[a[n],{n,0,nmax}] (* Jean-François Alcover, May 28 2024 *)

Formula

a(n) = A322280(n,n).

a(n) == n (mod 2) for n >= 1.