A366071 - OEIS

%I #13 Sep 29 2023 10:04:25

%S 1,0,0,1,-1,1,3,-8,14,1,-49,144,-162,-139,1159,-2532,2036,6062,-26282,

%T 47440,-11474,-190071,606163,-838984,-481092,5479390,-13618658,

%U 13030368,28786262,-148598623,294393355,-128639411,-1086088045,3848604261,-5935686369,-1750697623

%N Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x) ).

%F 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).

%o (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);

%Y Cf. A366095, A366096, A366097.

%Y Cf. A366101, A366102.

%Y Cf. A054514.

%K sign

%O 0,7

%A _Seiichi Manyama_, Sep 29 2023