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%I #9 Nov 05 2023 09:01:16
%S 1,2,4,8,18,52,184,688,2512,8864,30784,107648,384432,1403872,5205568,
%T 19443328,72817856,273199488,1027939072,3883718144,14741042464,
%U 56189409088,214931447680,824443822848,3169934397184,12214858010112,47168251137024
%N G.f. satisfies A(x) = 1 + 2*x*A(x) + 2*x^4*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/4)} 2^(n-3*k) * binomial(n,4*k) * A002293(k).
%o (PARI) a(n) = sum(k=0, n\4, 2^(n-3*k)*binomial(n, 4*k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A002293, A127902, A190590, A367114.
%Y Cf. A071356, A367113.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Nov 05 2023