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%I #8 Mar 14 2018 21:21:33
%S 1,1,0,1,0,0,2,-1,0,4,-6,6,6,-24,38,-17,-64,188,-230,-6,662,-1432,
%T 1286,1210,-6362,10692,-5530,-18274,57022,-74364,174,216703,-489544,
%U 467860,391258,-2256430,3948206,-2234064,-6725362,21920402,-29716570,2095564,84595798,-198418242,197499846
%N Signed recurrence over strict trees: a(n) = -1 + Sum_{y1 + ... + yk = n, y1 > ... > yk > 0, k > 1} a(y1) * ... * a(yk).
%t a[n_]:=a[n]=-1+Sum[Times@@a/@y,{y,Select[IntegerPartitions[n],Length[#]>1&&UnsameQ@@#&]}];
%t -Array[a,40]
%Y Cf. A000992, A018819, A063834, A099323, A196545, A220418, A273866, A273873, A289501, A290261, A300862, A300863, A300865, A300866.
%K sign
%O 1,7
%A _Gus Wiseman_, Mar 13 2018
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