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 A289079 Number of orderless same-trees of weight n with all leaves equal to 1. 20
 1, 1, 1, 2, 1, 3, 1, 5, 2, 3, 1, 13, 1, 3, 3, 22, 1, 16, 1, 15, 3, 3, 1, 151, 2, 3, 6, 17, 1, 41, 1, 334, 3, 3, 3, 637, 1, 3, 3, 275, 1, 56, 1, 21, 19, 3, 1, 15591, 2, 27, 3, 23, 1, 902, 3, 516, 3, 3, 1, 7858, 1, 3, 21, 69109, 3, 98, 1, 27, 3, 67, 1, 811756, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) is also the number of orderless same-trees of weight n with all leaves greater than 1. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA a(1) = 1, a(n>1) = Sum_{d|n, d>1} binomial(a(n/d)+d-1, d). EXAMPLE The a(12)=13 orderless same-trees with all leaves greater than 1 are: ((33)(33)), ((33)(222)), ((33)6), ((222)(222)), ((222)6), (66), ((22)(22)(22)), ((22)(22)4), ((22)44), (444), (3333), (222222), 12. MAPLE with(numtheory): a:= proc(n) option remember; `if`(n=1, 1, add(       binomial(a(n/d)+d-1, d), d=divisors(n) minus {1}))     end: seq(a(n), n=1..80);  # Alois P. Heinz, Jul 05 2017 MATHEMATICA a[n_]:=If[n===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)); v[1]=1; for(n=2, n, v[n] = sumdiv(n, d, binomial(v[n/d]+d-1, d))); v} \\ Andrew Howroyd, Aug 20 2018 (Python) from sympy import divisors, binomial l=[0, 1] for n in range(2, 101): l+=[sum([binomial(l[n//d] + d - 1, d) for d in divisors(n)[1:]]), ] l[1:] # Indranil Ghosh, Jul 06 2017 CROSSREFS Cf. A196545, A273873, A275870, A281145, A281146, A289078. Sequence in context: A296121 A277120 A104725 * A249810 A257111 A011129 Adjacent sequences:  A289076 A289077 A289078 * A289080 A289081 A289082 KEYWORD nonn AUTHOR Gus Wiseman, Jun 23 2017 STATUS approved

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Last modified August 8 05:25 EDT 2020. Contains 336290 sequences. (Running on oeis4.)