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a(n) = Sum_{k=0..n} (k/n)^2 * binomial(n,k)^5.
3

%I #9 Jul 14 2024 08:54:31

%S 1,9,136,2585,54126,1227492,29226688,723533337,18438032890,

%T 480994824134,12787403151744,345355150592036,9451729196625184,

%U 261628075707534720,7313361005558843136,206190939973811373593,5857313490484652859282

%N a(n) = Sum_{k=0..n} (k/n)^2 * binomial(n,k)^5.

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

%o (PARI) a(n) = sum(k=0, n-1, binomial(n-1, k)^2*binomial(n, k)^3);

%Y Cf. A005261, A374615, A374616.

%Y Cf. A181067, A198256.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 14 2024