A367032 G.f. satisfies A(x) = 1 + x*A(x)^2 - x^2*A(x)^5.
1, 1, 1, -2, -17, -57, -72, 386, 3007, 10239, 9205, -111000, -761932, -2419388, -810428, 36696186, 223335951, 638716047, -268768549, -12961722498, -70517888953, -176288334833, 256285732480, 4745735309240, 23204309443908, 48765510266948, -144850760459972
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n+k, k)*binomial(2*n, n-2*k)/(n+2*k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n+k,k) * binomial(2*n,n-2*k) / (n+2*k+1).