cp's OEIS Frontend

A294018 Number of strict trees whose leaves are the parts of the integer partition with Heinz number n.

%I A294018 #8 Feb 23 2018 09:58:06
%S A294018 0,1,1,0,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,0,1,1,3,1,0,1,1,
%T A294018 1,3,1,1,1,1,1,4,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,7,1,1,1,0,1,4,1,1,
%U A294018 1,3,1,6,1,1,1,1,1,4,1,1,0,1,1,8,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,3,1,4,1,1,4,1,1,6,1,4,1,1,1,4,1,1,1,1,1,13
%N A294018 Number of strict trees whose leaves are the parts of the integer partition with Heinz number n.
%C A294018 By convention a(1) = 0.
%C A294018 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%F A294018 A273873(n) = Sum_{i=1..A000041(n)} a(A215366(n,i)).
%e A294018 The a(84) = 8 strict trees: (((42)1)1), (((41)2)1), ((4(21))1), ((421)1), (((41)1)2), ((41)(21)), ((41)21), (4(21)1).
%t A294018 nn=120;
%t A294018 ptns=Table[If[n===1,{},Join@@Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]],{n,nn}];
%t A294018 tris=Join@@Map[Tuples[IntegerPartitions/@#]&,ptns];
%t A294018 qci[y_]:=qci[y]=If[Length[y]===1,1,Sum[Times@@qci/@t,{t,Select[tris,And[Length[#]>1,Sort[Join@@#,Greater]===y,UnsameQ@@Total/@#]&]}]];
%t A294018 qci/@ptns
%Y A294018 Cf. A000009, A000041, A000720, A001222, A056239, A063834, A196545, A215366, A273873, A281145, A289501, A296150, A299201, A299202, A299203.
%K A294018 nonn
%O A294018 1,30
%A A294018 _Gus Wiseman_, Feb 06 2018