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A318485
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Number of p-trees of weight 2n + 1 in which all outdegrees are odd.
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1
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1, 1, 2, 5, 13, 37, 107, 336, 1037, 3367, 10924, 36438, 121045, 412789, 1398168, 4831708, 16636297, 58084208, 202101971, 712709423, 2502000811, 8880033929, 31428410158, 112199775788, 399383181020, 1433385148187, 5128572792587, 18481258241133
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OFFSET
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0,3
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COMMENTS
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A p-tree of weight n with odd outdegrees is either a single node (if n = 1) or a finite odd-length sequence of at least 3 p-trees with odd outdegrees whose weights are weakly decreasing and sum to n.
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LINKS
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EXAMPLE
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The a(4) = 13 p-trees of weight 9 with odd outdegrees:
((((ooo)oo)oo)oo)
(((ooo)(ooo)o)oo)
(((ooo)oo)(ooo)o)
((ooo)(ooo)(ooo))
(((ooooo)oo)oo)
(((ooo)oooo)oo)
((ooooo)(ooo)o)
(((ooo)oo)oooo)
((ooo)(ooo)ooo)
((ooooooo)oo)
((ooooo)oooo)
((ooo)oooooo)
(ooooooooo)
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MATHEMATICA
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b[n_]:=b[n]=If[n>1, 0, 1]+Sum[Times@@b/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&]}];
Table[b[n], {n, 1, 20, 2}]
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PROG
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(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n] = polcoef(1/prod(k=1, n-1, 1 - v[k]*x^(2*k-1) + O(x^(2*n))) - 1/prod(k=1, n-1, 1 + v[k]*x^(2*k-1) + O(x^(2*n))), 2*n-1)/2); v} \\ Andrew Howroyd, Aug 27 2018
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CROSSREFS
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Cf. A027193, A063834, A078408, A196545, A279374, A289501, A298118, A300300, A300301, A300355, A300436, A300647, A300652, A300797, A302243.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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