A364744 - OEIS

%I #13 Aug 05 2023 10:32:29

%S 1,1,6,26,131,706,3932,22618,133099,797545,4850296,29859028,185712831,

%T 1165227025,7366475715,46877977451,300049605259,1930395961235,

%U 12476394685445,80968876247330,527424073700966,3447190219684125,22599794010813360

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

%H Seiichi Manyama, <a href="/A364744/b364744.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%Y Cf. A001006, A161634, A364742, A364743.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 05 2023