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

%I #13 Sep 29 2023 09:08:55

%S 1,2,7,29,132,637,3199,16536,87366,469556,2558610,14100033,78437805,

%T 439838596,2483300228,14103794518,80517436710,461768157262,

%U 2658979794811,15366500638407,89093023210674,518064484263918,3020484579372765,17653011431832906

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

%H Seiichi Manyama, <a href="/A366084/b366084.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%Y Cf. A049133, A243157, A366085.

%Y Cf. A366052.

%K sign

%O 0,2

%A _Seiichi Manyama_, Sep 28 2023