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Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x-x^2) ).
3

%I #15 Sep 30 2023 09:18:45

%S 1,1,1,0,-5,-22,-68,-165,-285,-96,1892,10574,38436,107175,217063,

%T 165232,-1150565,-7780744,-31173680,-94537100,-212903852,-239418048,

%U 788015576,6734057510,29396759220,95418332383,233697161887,334222633632,-514863450175,-6299672869750

%N Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x-x^2) ).

%H Seiichi Manyama, <a href="/A366081/b366081.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+1,k) * binomial(2*n-k,n-2*k).

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, k)*binomial(2*n-k, n-2*k))/(n+1);

%Y Cf. A007440, A108623, A366082, A366083.

%Y Cf. A109081.

%K sign

%O 0,5

%A _Seiichi Manyama_, Sep 28 2023