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Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x-x^2) ).
3

%I #13 Sep 29 2023 09:27:53

%S 1,3,14,78,478,3109,21063,146997,1049302,7624330,56198481,419155136,

%T 3157356819,23984387314,183519131353,1413099475142,10941294442694,

%U 85132006090350,665294548097852,5219591907202092,41095469624286421,324595783790966343

%N Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x-x^2) ).

%H Seiichi Manyama, <a href="/A366083/b366083.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(4*n-k+2,n-2*k).

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, k)*binomial(4*n-k+2, n-2*k))/(n+1);

%Y Cf. A007440, A108623, A366081, A366082.

%Y Cf. A366050.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 28 2023