A036250 Number of trees of nonempty sets with n points. (Each node is a set of 1 or more points.)

1, 1, 2, 3, 7, 14, 35, 85, 231, 633, 1845, 5461, 16707, 51945, 164695, 529077, 1722279, 5664794, 18813369, 62996850, 212533226, 721792761, 2466135375, 8471967938, 29249059293, 101440962296, 353289339927, 1235154230060, 4333718587353, 15255879756033

Offset: 0

Author

Christian G. Bower, Nov 15 1998

Keywords

• nonn

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.
• Gus Wiseman, Non-isomorphic representatives of the a(1) = 2 through a(5) = 35 connected multigraphs with loops with multiset density -1.
• Index entries for sequences related to trees

Crossrefs

Essentially the same as A036251.

Cf. A000055, A007718, A007719, A038052, A191646, A303837, A321155, A321229, A321254, A321256, A322111.

Programs

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 *)

Formula

G.f.: B(x) - B^2(x)/2 + B(x^2)/2, where B(x) is g.f. for A036249.