%I #19 Sep 02 2023 10:35:22
%S 1,1,6,50,485,5130,57391,667777,7999095,97986680,1221813880,
%T 15456556791,197887386913,2559189842240,33383097891135,
%U 438714241508615,5803049210371375,77199163872173757,1032215519193531310,13864180990526161995,186975433988014039830
%N G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^5).
%H Seiichi Manyama, <a href="/A365189/b365189.txt">Table of n, a(n) for n = 0..864</a>
%F a(n) = (1/(5*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(5*n+1,n-k).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(5*n+1, n-k))/(5*n+1);
%Y Cf. A002295, A365184, A365185, A365186, A365187, A365188.
%Y Cf. A006605, A255673, A365183.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023