%I #12 Aug 27 2018 16:21:57

%S 1,1,1,0,1,0,0,1,0,0,1,-1,1,1,-2,3,-1,-3,8,-8,1,14,-26,22,10,-59,90,

%T -52,-74,238,-291,80,417,-930,915,124,-1991,3483,-2533,-2148,9011,

%U -12596,5754,14350,-37975,42735,-4046,-77924,154374,-133903,-56529,376844,-591197,355941,522978,-1706239

%N Signed recurrence over binary strict trees: a(n) = 1 - Sum_{x + y = n, 0 < x < y < n} a(x) * a(y).

%H Andrew Howroyd, <a href="/A300866/b300866.txt">Table of n, a(n) for n = 0..500</a>

%t a[n_]:=a[n]=1-Sum[a[k]*a[n-k],{k,1,(n-1)/2}];

%t Array[a,40]

%o (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 - sum(k=1, (n-1)\2, v[k]*v[n-k])); concat([1], v)} \\ _Andrew Howroyd_, Aug 27 2018

%Y Cf. A000992, A001190, A007317, A063834, A099323, A196545, A220418, A273866, A273873, A289501, A290261, A300442, A300443, A300862, A300863, A300864, A300865.

%K sign

%O 0,15

%A _Gus Wiseman_, Mar 13 2018