A300866 - OEIS

A300866

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

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, -52, -74, 238, -291, 80, 417, -930, 915, 124, -1991, 3483, -2533, -2148, 9011, -12596, 5754, 14350, -37975, 42735, -4046, -77924, 154374, -133903, -56529, 376844, -591197, 355941, 522978, -1706239

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OFFSET

0,15

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

MATHEMATICA

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

Array[a, 40]

PROG

(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

CROSSREFS