A365756 - OEIS

%I #8 Sep 18 2023 08:58:59

%S 1,1,1,1,2,7,22,58,142,363,1014,2966,8645,24824,71189,206742,609159,

%T 1809493,5388804,16073002,48092377,144532884,436168716,1320372837,

%U 4006489208,12183544414,37132838866,113426618425,347191793705,1064688271730,3270387354434

%N G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^3*A(x)^4).

%F a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(n+k+1,n-3*k) / (n+k+1).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(n+k+1, n-3*k)/(n+k+1));

%Y Cf. A023432, A212383, A365243, A365757.

%Y Cf. A063019.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 18 2023