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

%I #9 Sep 28 2023 12:07:45

%S 1,1,2,5,13,35,96,264,719,1913,4875,11478,22860,26044,-77216,-793820,

%T -4394125,-20304455,-85805571,-343282020,-1321898694,-4943906064,

%U -18052305410,-64551823869,-226418611750,-779487689870,-2633172840764,-8717790419014

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+1,k) * binomial(2*n-3*k,n-4*k).

%o (PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n+1, k)*binomial(2*n-3*k, n-4*k))/(n+1);

%Y Cf. A366086, A366087, A366089, A366090.

%Y Cf. A366054.

%K sign

%O 0,3

%A _Seiichi Manyama_, Sep 28 2023