%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