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%I #12 Jun 24 2018 03:13:00
%S 1,0,2,2,6,14,34,82,214,566,1482,4058,10950,30406,83786,235714,658286,
%T 1874254,5293674,15189810,43312542,125075238,359185586,1043712922,
%U 3015569582,8800146182,25565402802,74918274562,218572345718,642783954238,1882606578002
%N Signed recurrence over enriched p-trees: a(n) = (-1)^(n - 1) + Sum_{y1 + ... + yk = n, y1 >= ... >= yk > 0, k > 1} a(y1) * ... * a(yk).
%H Seiichi Manyama, <a href="/A300863/b300863.txt">Table of n, a(n) for n = 1..500</a>
%F O.g.f.: (-1/(1+x) + Product 1/(1-a(n)x^n))/2.
%t a[n_]:=a[n]=(-1)^(n-1)+Sum[Times@@a/@y,{y,Select[IntegerPartitions[n],Length[#]>1&]}];
%t Array[a,40]
%Y Cf. A000992, A063834, A099323, A196545, A220418, A273866, A273873, A289501, A290261, A300862, A300864, A300865, A300866.
%K nonn
%O 1,3
%A _Gus Wiseman_, Mar 13 2018
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