A371521 - OEIS

%I #15 Mar 27 2024 08:53:56

%S 1,6,57,614,7158,88002,1123689,14760024,198172050,2707560544,

%T 37522666803,526190125308,7452866846847,106465245105972,

%U 1532129408941797,22191180837313808,323243244688652943,4732225866305323686,69591395772704207770,1027547992261749954798

%N G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^6.

%F a(n) = 6 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+5,k)/(5*k+6) = Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+6,k)/(k+1).

%F G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A349333.

%o (PARI) a(n) = 6*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+5, k)/(5*k+6));

%Y Cf. A349333, A371379, A371519, A371522, A371523.

%Y Cf. A045868, A371516, A371517, A371520.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 26 2024