Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #9 Nov 05 2023 09:01:00
%S 1,2,4,8,17,42,124,408,1380,4616,15184,49568,162518,539580,1818184,
%T 6203088,21339916,73776024,255853744,889678688,3102779785,10856555130,
%U 38115293308,134243564056,474159194316,1678926445272,5957812156144,21183679310048
%N G.f. satisfies A(x) = 1 + 2*x*A(x) + x^4*A(x)^4.
%F a(n) = Sum_{k=0..floor(n/4)} 2^(n-4*k) * binomial(n,4*k) * A002293(k).
%o (PARI) a(n) = sum(k=0, n\4, 2^(n-4*k)*binomial(n, 4*k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A002293, A127902, A190590, A367115.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Nov 05 2023