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%I #15 Sep 09 2024 09:35:28
%S 1,0,-1,3,-4,-9,73,-212,111,1956,-10078,21466,29823,-418183,1561911,
%T -1722963,-13205004,86962328,-232448945,-109578204,3849218852,
%U -17135183489,27800381006,113891855632,-966644138742,3075070731677,-833503324311,-41673632701038
%N G.f. satisfies A(x) = (1 + x*A(x)) * (1 - x*A(x)^4).
%F a(n) = Sum_{k=0..n} (-1)^k * binomial(n+3*k+1,k) * binomial(n+3*k+1,n-k) / (n+3*k+1).
%F G.f.: x/series_reversion(x*G(x)), where G(x) = 1 - x^2 + 3*x^3 - 6*x^4 + 6*x^5 + 15*x^6 - ... is the g.f. of A364372. - _Peter Bala_, Aug 27 2024
%o (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+3*k+1, k)*binomial(n+3*k+1, n-k)/(n+3*k+1));
%Y Cf. A364372, A364374, A364375.
%Y Cf. A215623.
%K sign,easy
%O 0,4
%A _Seiichi Manyama_, Jul 21 2023