A364827 - OEIS

%I #17 Aug 09 2023 16:57:19

%S 1,2,26,478,10254,240122,5950530,153417542,4072868742,110585691634,

%T 3056671795946,85722961493742,2433127206219582,69763483031049066,

%U 2017643094336224914,58789801741123032918,1724199860717303739062,50858327392484088101346

%N G.f. satisfies A(x) = 1 - x*A(x)^5 * (1 - 3*A(x)).

%H Seiichi Manyama, <a href="/A364827/b364827.txt">Table of n, a(n) for n = 0..666</a>

%F a(n) = (-1)^n * Sum_{k=0..n} (-3)^k * binomial(n,k) * binomial(5*n+k+1,n) / (5*n+k+1).

%F a(n) = (1/n) * Sum_{k=0..n-1} 2^(n-k) * binomial(n,k) * binomial(6*n-k,n-1-k) for n > 0.

%F a(n) = (1/n) * Sum_{k=1..n} 2^k * 3^(n-k) * binomial(n,k) * binomial(5*n,k-1) for n > 0.

%o (PARI) a(n) = (-1)^n*sum(k=0, n, (-3)^k*binomial(n, k)*binomial(5*n+k+1, n)/(5*n+k+1));

%Y Cf. A025192, A107841, A235347, A364825, A364826.

%Y Cf. A243668, A363006.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 09 2023