A340024 Number of inequivalent vertex colorings of graphs on n unlabeled vertices.

1, 1, 4, 14, 89, 788, 13712, 459380, 31395800, 4304547500, 1170501781632, 626269787446920, 657129205489027200, 1350883625562244545584, 5441806297331472273603040, 42987375826579901036722653600, 666538741644051928632441002162384, 20306710978262167791045247702178986496

Offset: 0

Author

Andrew Howroyd, Jan 01 2021

Keywords

• nonn

Comments

Equivalence is up to permutation of the colors. Adjacent vertices may have the same color.

Crossrefs

Cf. A000088, A340022, A340023, A340027.

Programs

PARI

\\ See links in A339645 for combinatorial species functions.
edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
graphsCycleIndex(n)={my(s=0); forpart(p=n, s+=permcount(p) * 2^edges(p) * sMonomial(p)); s/n!}
graphsSeries(n)={sum(k=0, n, graphsCycleIndex(k)*x^k) + O(x*x^n)}
InequivalentColoringsSeq(graphsSeries(15))