A366101 Expansion of (1/x) * Series_Reversion( x*(1+x-x^5)/(1+x) ).
1, 0, 0, 0, 0, 1, -1, 1, -1, 1, 5, -12, 20, -29, 39, 1, -109, 305, -611, 1051, -1145, 139, 3055, -9924, 22424, -37574, 43476, -14035, -97831, 368715, -852385, 1470767, -1823523, 885634, 3444224, -14239745, 34089723, -61051093, 80200515, -48234695, -123155951
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\5, (-1)^(n-k)*binomial(n+k, k)*binomial(n-4*k-1, n-5*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} (-1)^(n-k) * binomial(n+k,k) * binomial(n-4*k-1,n-5*k).