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Expansion of (1/x) * Series_Reversion( x*(1+x+x^4)/(1+x) ).
2

%I #9 Sep 29 2023 10:04:59

%S 1,0,0,0,-1,1,-1,1,4,-10,17,-25,-1,76,-217,443,-490,-94,1999,-6208,

%T 11527,-12350,-4471,63826,-184055,332713,-342399,-231390,2101215,

%U -5790892,10230983,-9625472,-10237792,71714387,-190381165,324440310,-275119412,-430340403

%N Expansion of (1/x) * Series_Reversion( x*(1+x+x^4)/(1+x) ).

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^(n-k) * binomial(n+k,k) * binomial(n-3*k-1,n-4*k).

%o (PARI) a(n) = sum(k=0, n\4, (-1)^(n-k)*binomial(n+k, k)*binomial(n-3*k-1, n-4*k))/(n+1);

%Y Cf. A366071, A366101.

%K sign

%O 0,9

%A _Seiichi Manyama_, Sep 29 2023