A366071 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x) ).
1, 0, 0, 1, -1, 1, 3, -8, 14, 1, -49, 144, -162, -139, 1159, -2532, 2036, 6062, -26282, 47440, -11474, -190071, 606163, -838984, -481092, 5479390, -13618658, 13030368, 28786262, -148598623, 294393355, -128639411, -1086088045, 3848604261, -5935686369, -1750697623
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, (-1)^(n-k)*binomial(n+k, k)*binomial(n-2*k-1, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^(n-k) * binomial(n+k,k) * binomial(n-2*k-1,n-3*k).