A366116 Expansion of (1/x) * Series_Reversion( x*(1+x+x^3)/(1+x)^2 ).
1, 1, 1, 0, -3, -9, -15, -7, 50, 203, 429, 382, -1045, -5845, -14751, -18627, 20255, 184818, 549630, 879632, -156085, -6025489, -21267251, -40911195, -17629620, 193929269, 835617523, 1881543582, 1674869775, -5855762293, -32848801375, -85601962056, -108647926359
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, (-1)^k*binomial(n+k, k)*binomial(n-k+1, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n+k,k) * binomial(n-k+1,n-3*k).