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 A318485 Number of p-trees of weight 2n + 1 in which all outdegrees are odd. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 EXAMPLE 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) MATHEMATICA 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}] PROG (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 CROSSREFS Cf. A027193, A063834, A078408, A196545, A279374, A289501, A298118, A300300, A300301, A300355, A300436, A300647, A300652, A300797, A302243. Sequence in context: A233281 A218551 A293297 * A005961 A036249 A126031 Adjacent sequences:  A318482 A318483 A318484 * A318486 A318487 A318488 KEYWORD nonn AUTHOR Gus Wiseman, Aug 27 2018 STATUS approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)