A371495 - OEIS

%I #8 Mar 25 2024 09:21:31

%S 1,3,12,64,381,2430,16227,112008,792717,5721165,41945373,311529831,

%T 2338909219,17722127580,135346614906,1040779011412,8051611785006,

%U 62620659604659,489339248275242,3840135625895886,30251386980891657,239138782521553659,1896380840948325606

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(4*k+2,k)/(k+1).

%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(4*k+2, k)/(k+1));

%Y Cf. A001006, A371494, A371496.

%Y Cf. A006632.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 25 2024