A363982 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 + x*A(x)^3).
1, 1, 1, -1, -8, -16, 16, 195, 491, -317, -6293, -18608, 4610, 230385, 780625, 107615, -9028280, -34695607, -17401607, 367885509, 1598468196, 1350497961, -15317000747, -75391402496, -88375867528, 643505487144, 3611942077216, 5376931884971
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(2*n+k, n-1-k))/n);
Formula
a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(2*n+k,n-1-k) for n > 0.