cp's OEIS Frontend

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

%I A036250 #30 Jan 28 2019 05:52:30
%S A036250 1,1,2,3,7,14,35,85,231,633,1845,5461,16707,51945,164695,529077,
%T A036250 1722279,5664794,18813369,62996850,212533226,721792761,2466135375,
%U A036250 8471967938,29249059293,101440962296,353289339927,1235154230060,4333718587353,15255879756033
%N A036250 Number of trees of nonempty sets with n points. (Each node is a set of 1 or more points.)
%C A036250 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
%H A036250 Alois P. Heinz, <a href="/A036250/b036250.txt">Table of n, a(n) for n = 0..1717</a>
%H A036250 Richard J. Mathar, <a href="https://arxiv.org/abs/1808.06264">Counting Connected Graphs without Overlapping Cycles</a>, arXiv:1808.06264 [math.CO], 2018.
%H A036250 Gus Wiseman, <a href="/A036250/a036250.png">Non-isomorphic representatives of the a(1) = 2 through a(5) = 35 connected multigraphs with loops with multiset density -1.</a>
%H A036250 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A036250 G.f.: B(x) - B^2(x)/2 + B(x^2)/2, where B(x) is g.f. for A036249.
%t A036250 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 *)
%Y A036250 Essentially the same as A036251.
%Y A036250 Cf. A000055, A007718, A007719, A038052, A191646, A303837, A321155, A321229, A321254, A321256, A322111.
%K A036250 nonn
%O A036250 0,3
%A A036250 _Christian G. Bower_, Nov 15 1998