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 A299203 Number of enriched p-trees whose multiset of leaves is the integer partition with Heinz number n. 18
 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 5, 1, 3, 1, 3, 1, 1, 1, 11, 1, 1, 2, 3, 1, 5, 1, 12, 1, 1, 1, 15, 1, 1, 1, 11, 1, 4, 1, 3, 3, 1, 1, 38, 1, 3, 1, 3, 1, 9, 1, 9, 1, 1, 1, 21, 1, 1, 4, 34, 1, 4, 1, 3, 1, 5, 1, 54, 1, 1, 3, 3, 1, 4, 1, 33, 5, 1, 1, 23, 1, 1, 1, 9, 1, 20, 1, 3, 1, 1, 1, 117, 1, 3, 3, 12, 1, 4, 1, 9, 4, 1, 1, 57, 1, 4, 1, 34 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS By convention, a(1) = 0. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS EXAMPLE a(54) = 9: (((22)2)1), ((222)1), (((22)1)2), (((21)2)2), ((221)2), ((22)(21)), ((22)21), ((21)22), (2221). a(40) = 11: ((31)(11)), (((31)1)1), ((3(11))1), ((311)1), (3((11)1)), (3(111)), (((11)1)3), ((111)3), ((31)11), (3(11)1), (3111). a(36) = 15: ((22)(11)), ((2(11))2), (((11)2)2), (((21)1)2), ((211)2), (((22)1)1), (((21)2)1), ((221)1), ((21)(21)), (22(11)), (2(11)2), ((11)22), ((22)11), ((21)21), (2211). MATHEMATICA nn=120; ptns=Table[If[n===1, {}, Join@@Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]], {n, nn}]; tris=Join@@Map[Tuples[IntegerPartitions/@#]&, ptns]; qci[y_]:=qci[y]=If[Length[y]===1, 1, Sum[Times@@qci/@t, {t, Select[tris, And[Length[#]>1, Sort[Join@@#, Greater]===y]&]}]]; qci/@ptns CROSSREFS Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299200, A299201, A299202. Sequence in context: A010121 A174726 A300239 * A329036 A205552 A255707 Adjacent sequences:  A299200 A299201 A299202 * A299204 A299205 A299206 KEYWORD nonn AUTHOR Gus Wiseman, Feb 05 2018 STATUS approved

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Last modified January 22 10:52 EST 2020. Contains 331144 sequences. (Running on oeis4.)