cp's OEIS Frontend

A300355 Number of enriched p-trees of weight n with odd leaves.

%I A300355 #9 Aug 26 2018 16:32:49
%S A300355 1,1,1,3,6,16,47,132,410,1254,4052,12818,42783,139082,469924,1563606,
%T A300355 5353966,18065348,62491018,213391790,743836996,2565135934,8994087070,
%U A300355 31251762932,110245063771,385443583008,1365151504722,4800376128986,17070221456536,60289267885410
%N A300355 Number of enriched p-trees of weight n with odd leaves.
%C A300355 An enriched p-tree of weight n > 0 is either a single node of weight n, or a sequence of two or more enriched p-trees with weakly decreasing weights summing to n.
%H A300355 Andrew Howroyd, <a href="/A300355/b300355.txt">Table of n, a(n) for n = 0..500</a>
%F A300355 O.g.f: (1 + x/(1-x^2) + Prod_{i>0} 1/(1 - a(i)x^i))/2.
%F A300355 a(n) = Sum_{i=1..A000009(n)} A299203(A300351(n,i)).
%e A300355 The a(5) = 16 enriched p-trees of weight with odd leaves:
%e A300355 5,
%e A300355 ((31)1), ((((11)1)1)1), (((111)1)1), (((11)(11))1), (((11)11)1), ((1111)1),
%e A300355 (3(11)), (((11)1)(11)), ((111)(11)),
%e A300355 (311), (((11)1)11), ((111)11),
%e A300355 ((11)(11)1),
%e A300355 ((11)111),
%e A300355 (11111).
%t A300355 c[n_]:=c[n]=If[EvenQ[n],0,1]+Sum[Times@@c/@y,{y,Select[IntegerPartitions[n],Length[#]>1&]}];
%t A300355 Table[c[n],{n,30}]
%o A300355 (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = n%2 + polcoef(1/prod(k=1, n-1, 1 - v[k]*x^k + O(x*x^n)), n)); concat([1], v)} \\ _Andrew Howroyd_, Aug 26 2018
%Y A300355 Cf. A000009, A063834, A078408, A089259, A196545, A279374, A279785, A289501, A294079, A299202, A299203, A300300, A300301, A300352, A300353, A300354.
%K A300355 nonn
%O A300355 0,4
%A A300355 _Gus Wiseman_, Mar 03 2018