A371889 - OEIS

%I #6 Apr 11 2024 10:10:27

%S 1,1,2,2,-1,-4,7,33,-5,-200,-151,1185,2202,-6069,-21799,21791,182718,

%T 26520,-1349611,-1613331,8674338,21651795,-44750412,-217666394,

%U 121538304,1859974399,1023915107,-13828122997,-23155237537,86925632115,282182920662

%N G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^3).

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

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

%Y Cf. A243156, A307678, A364747, A365192.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 11 2024