OFFSET
0,3
COMMENTS
Also the number of non-isomorphic connected multigraphs with loops with n edges and multiset density -1, where the multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices. - Gus Wiseman, Nov 28 2018
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1717
Richard J. Mathar, Counting Connected Graphs without Overlapping Cycles, arXiv:1808.06264 [math.CO], 2018.
FORMULA
G.f.: B(x) - B^2(x)/2 + B(x^2)/2, where B(x) is g.f. for A036249.
MATHEMATICA
max = 30; B[_] = 1; Do[B[x_] = x*Exp[Sum[(B[x^k] + x^k)/k + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; A[x_] = B[x] - B[x]^2/2 + B[x^2]/2; CoefficientList[1 + A[x] + O[x]^max, x] (* Jean-François Alcover, Jan 28 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Nov 15 1998
STATUS
approved