OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
a(2) = 2 because there is 1 connected graph on 2 vertices which can either have both vertices labeled 1 or one vertex labeled 1 and the other 2.
a(3) = 12 because there are 2 connected graphs on 3 vertices. The complete graph K_3 can be labeled in 4 ways (111, 112, 122, 123) and the path graph P_3 can be labeled in 8 ways (111, 112, 121, 122, 212, 123, 132, 213).
PROG
(PARI) \\ See A340023 for G(n, k).
InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v, n, polcoef(p, n)), vector(#v, n, 1/n))}
seq(n)={my(v=concat([1], InvEulerT(vector(n, n, G(n, y))))); sum(k=0, n, subst(v, y, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 02 2021
STATUS
approved