A367031 G.f. satisfies A(x) = 1 + x*A(x)^2 - x^2*A(x)^4.
1, 1, 1, -1, -10, -33, -55, 65, 842, 3230, 6137, -6631, -102166, -421705, -864225, 795615, 14526042, 63072042, 136736102, -102140350, -2256842380, -10210904245, -23195817445, 13298317815, 371005984450, 1740942920122, 4120912606657, -1666840127743
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n, k)*binomial(2*n-k, n-2*k)/(n+k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n,k) * binomial(2*n-k,n-2*k) / (n+k+1).