A364734 - OEIS

%I #13 Aug 05 2023 13:12:01

%S 1,1,2,9,48,276,1687,10750,70597,474478,3247844,22563904,158693152,

%T 1127661358,8083795761,58390722901,424562043703,3104994695198,

%U 22825260066996,168564068029385,1249985066423749,9303815610715531,69483859839881494,520527161650519576

%N G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^5).

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

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

%Y Cf. A000108, A106228, A300048, A364723.

%Y Cf. A364740.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 05 2023