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A036250 Number of trees of nonempty sets with n points. (Each node is a set of 1 or more points.) 6
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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-Fran├žois Alcover, Jan 28 2019 *)

CROSSREFS

Essentially the same as A036251.

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

Sequence in context: A185089 A180564 A113822 * A191491 A210345 A006660

Adjacent sequences:  A036247 A036248 A036249 * A036251 A036252 A036253

KEYWORD

nonn

AUTHOR

Christian G. Bower, Nov 15 1998

STATUS

approved

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Last modified January 21 08:09 EST 2020. Contains 331104 sequences. (Running on oeis4.)