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A300650 Number of orderless same-trees of weight 2n + 1 in which all outdegrees are odd and all leaves greater than 1. 3
1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 6, 1, 1, 3, 3, 1, 3, 1, 1, 19, 1, 2, 3, 1, 3, 3, 1, 1, 21, 3, 1, 3, 1, 1, 28, 3, 1, 68, 1, 3, 3, 1, 3, 3, 3, 1, 25, 1, 1, 71, 1, 1, 3, 1, 3, 27, 3, 2, 3, 8, 1, 3, 1, 3, 1656, 1, 1, 3, 3, 3, 43, 1, 1, 31, 3, 1, 3, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
An orderless same-tree of weight n > 0 is either a single node of weight n, or a finite multiset of two or more orderless same-trees whose weights are all equal and sum to n.
LINKS
FORMULA
a(1) = 1; a(n > 1) = Sum_d binomial(a(n/d) + d - 1, d) where the sum is over odd divisors of n greater than 1.
EXAMPLE
The a(13) = 6 orderless same-trees: 27, (999), (99(333)), (9(333)(333)), ((333)(333)(333)), (333333333).
MATHEMATICA
a[n_]:=If[n===1, 1, Sum[Binomial[a[n/d]+d-1, d], {d, Select[Rest[Divisors[n]], OddQ]}]];
Table[a[n], {n, 1, 100, 2}]
PROG
(PARI) f(n) = if (n==1, 1, sumdiv(n, d, if ((d > 1) && (d % 2), binomial(f(n/d)+d-1, d))));
a(n) = f(2*n+1); \\ Michel Marcus, Mar 10 2018
CROSSREFS
Sequence in context: A232529 A095374 A352063 * A363528 A300649 A086599
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 10 2018
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)