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%I #10 May 31 2021 17:46:37
%S 1,1,2,1,2,2,2,1,6,2,2,2,2,2,12,1,2,6,2,2,14,2,2,2,8,2,68,2,2,12,2,1,
%T 18,2,16,6,2,2,20,2,2,14,2,2,644,2,2,2,10,8,24,2,2,68,20,2,26,2,2,12,
%U 2,2,1386,1,22,18,2,2,30,16,2,6,2,2,4532,2,22,20
%N Number of orderless same-trees of weight n in which all outdegrees are odd.
%C 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.
%H Antti Karttunen, <a href="/A300648/b300648.txt">Table of n, a(n) for n = 1..8192</a>
%F a(n) = 1 + Sum_d binomial(a(n/d) + d - 1, d) where the sum is over odd divisors of n greater than 1.
%e The a(9) = 6 odd orderless same-trees: 9, (333), (33(111)), (3(111)(111)), ((111)(111)(111)), (111111111).
%t a[n_]:=1+Sum[Binomial[a[n/d]+d-1,d],{d,Select[Rest[Divisors[n]],OddQ]}];
%t Array[a,80]
%o (PARI) a(n) = if (n==1, 1, 1 + sumdiv(n, d, if ((d > 1) && (d % 2), binomial(a(n/d) + d - 1, d)))); \\ _Michel Marcus_, Mar 10 2018
%Y Cf. A003238, A006241, A063834, A069283, A273873, A281145, A289078, A289079, A289501, A298118, A300436, A300439, A300574, A300647, A300649, A300650.
%K nonn,look
%O 1,3
%A _Gus Wiseman_, Mar 10 2018
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