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%I #12 Feb 07 2021 00:41:59
%S 1,1,8,117,2800,97125,4551876,274975897,20690260928,1889451727497,
%T 205192914235300,26068434774065541,3822244304373085680,
%U 639508508456359098349,120922358829574588363364,25626415609908102483018225
%N a(n) = Sum_{k=0..n} k^n * (n-k)! * binomial(n,k)^2.
%t a[0] = 1; a[n_] := Sum[k^n * (n-k)! * Binomial[n, k]^2, {k, 0, n}]; Array[a, 16, 0] (* _Amiram Eldar_, Feb 06 2021 *)
%o (PARI) a(n) = sum(k=0, n, k^n*(n-k)!*binomial(n, k)^2);
%Y Main diagonal of A341200.
%Y Cf. A277373, A341185.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 06 2021