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a(n) = (n!)^3 * Sum_{k=0..n} (k/k!)^3.
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%I #13 Jan 05 2024 07:56:45

%S 0,1,16,459,29440,3680125,794907216,272653175431,139598425821184,

%T 101767252423643865,101767252423643866000,135452212975869985647331,

%U 234061424022303335198589696,514232948577000427431301564309,1411055210895289172871491492466640

%N a(n) = (n!)^3 * Sum_{k=0..n} (k/k!)^3.

%F a(0) = 0; a(n) = n^3 * a(n-1) + n^3.

%F a(n) = n^3 * A217284(n-1) for n > 0.

%o (PARI) a(n) = n!^3*sum(k=0, n, (k/k!)^3);

%Y Cf. A368769, A368770, A368771.

%Y Cf. A193563, A217284.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Jan 05 2024