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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

Table of n, a(n) for n=0..81.

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

Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300647, A300648, A300649.

Sequence in context: A030360 A232529 A095374 * A300649 A086599 A181846

Adjacent sequences:  A300647 A300648 A300649 * A300651 A300652 A300653

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 10 2018

STATUS

approved

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Last modified July 4 14:15 EDT 2020. Contains 335448 sequences. (Running on oeis4.)