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 A289078 Number of orderless same-trees of weight n. 26
 1, 2, 2, 5, 2, 9, 2, 22, 6, 11, 2, 94, 2, 13, 12, 334, 2, 205, 2, 210, 14, 17, 2, 7218, 8, 19, 68, 443, 2, 1687, 2, 69109, 18, 23, 16, 167873, 2, 25, 20, 89969, 2, 7041, 2, 1548, 644, 29, 2, 36094795, 10, 3078, 24, 2604, 2, 1484102, 20, 1287306, 26, 35, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS An orderless same-tree t is either: (case 1) a positive integer, or (case 2) a finite multiset of two or more orderless same-trees, all having the same weight. The weight of t in case 1 is the number itself, and in case 2 it is the sum of weights of the branches. For example {{{3,{1,1,1}},{2,{1,1},{1,1}}},{{{1,1,1},{1,1,1}},{{1,1},{1,1},{1,1}}}} is an orderless same-tree of weight 24 with 2 branches. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..2500 FORMULA a(n) = 1 + Sum_{d|n, d>1} binomial(a(n/d)+d-1, d). EXAMPLE The a(6)=9 orderless same-trees are: 6, (33), (3(111)), (222), (22(11)), (2(11)(11)), ((11)(11)(11)), ((111)(111)), (111111). MAPLE with(numtheory): a:= proc(n) option remember; 1 + add(       binomial(a(n/d)+d-1, d), d=divisors(n) minus {1})     end: seq(a(n), n=1..60);  # Alois P. Heinz, Jul 05 2017 MATHEMATICA a[n_]:=If[n===1, 1, 1+Sum[Binomial[a[n/d]+d-1, d], {d, Rest[Divisors[n]]}]]; Array[a, 100] PROG (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + sumdiv(n, d, binomial(v[n/d]+d-1, d))); v} \\ Andrew Howroyd, Aug 20 2018 CROSSREFS Cf. A196545, A273873, A275870, A281145, A281146, A289079. Sequence in context: A305798 A305808 A266662 * A051612 A083456 A211932 Adjacent sequences:  A289075 A289076 A289077 * A289079 A289080 A289081 KEYWORD nonn AUTHOR Gus Wiseman, Jun 23 2017 STATUS approved

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Last modified August 5 08:27 EDT 2021. Contains 346464 sequences. (Running on oeis4.)