A366095 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^2 ).
1, 1, 1, 2, 5, 11, 25, 63, 162, 415, 1085, 2896, 7795, 21127, 57785, 159253, 441351, 1229506, 3442150, 9678358, 27315923, 77364683, 219815829, 626375327, 1789627564, 5125729137, 14714078483, 42327358520, 121998755959, 352272227623, 1018915014521
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, 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)} binomial(n+k,k) * binomial(n-k+1,n-3*k).