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%I #15 Nov 03 2023 11:18:24
%S 1,1,5,26,168,1195,8988,70318,566388,4665221,39113732,332691758,
%T 2863778072,24900264326,218372530380,1929363592870,17157018725000,
%U 153442147343648,1379250344938676,12453816724761706,112907775890596400,1027394297869071687
%N G.f. satisfies A(x) = 1 + x^2 + x*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*(n-2*k)+1,k) * binomial(4*(n-2*k),n-2*k)/(3*(n-2*k)+1).
%o (PARI) a(n) = sum(k=0, n\2, binomial(3*(n-2*k)+1, k)*binomial(4*(n-2*k), n-2*k)/(3*(n-2*k)+1));
%Y Cf. A176697, A367040.
%Y Cf. A365178, A365180, A365181, A365182, A365183, A367048, A367049, A367050.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 03 2023
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