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

%I #9 Sep 29 2023 10:04:46

%S 1,2,5,14,43,143,507,1885,7247,28523,114190,463179,1898892,7855615,

%T 32754687,137520639,580920600,2467305352,10530055735,45135757683,

%U 194224957674,838729701308,3633559928326,15787558766909,68780335280091,300391273651651,1314927603572310

%N Expansion of (1/x) * Series_Reversion( x*(1+x-x^4)/(1+x)^3 ).

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

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

%Y Cf. A366098, A366100.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 29 2023