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%I #13 Mar 12 2023 10:58:22
%S 1,2,6,20,70,250,912,3372,12590,47362,179230,681528,2601896,9966798,
%T 38288420,147453664,569092438,2200577502,8523612766,33064771524,
%U 128438624798,499525018638,1944918241388,7580283784548,29571439970136,115459524588322,451157870454298
%N a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).
%H Seiichi Manyama, <a href="/A360295/b360295.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: 1 / sqrt(1-4*x/(1+x^4)).
%F n*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-4)*a(n-4) + 2*(2*n-13)*a(n-5) - (n-8)*a(n-8).
%o (PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n-1-3*k, k)*binomial(2*n-8*k, n-4*k));
%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x^4)))
%Y Cf. A360293, A360294.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 01 2023
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