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a(n) = (n!)^3 * Sum_{k=0..n} k^2/(k!)^3.
4

%I #11 Jan 05 2024 07:56:49

%S 0,1,12,333,21328,2666025,575861436,197520472597,101130481969728,

%T 73724121355931793,73724121355931793100,98126805524745216616221,

%U 169563119946759734312830032,372530174523031136285287580473,1022222798891197437966829120818108

%N a(n) = (n!)^3 * Sum_{k=0..n} k^2/(k!)^3.

%F a(0) = 0; a(n) = n^3 * a(n-1) + n^2.

%F a(n) = n^2 * A368775(n-1) for n > 0.

%o (PARI) a(n) = n!^3*sum(k=0, n, k^2/k!^3);

%Y Cf. A368769, A368770, A368772.

%Y Cf. A368775.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 05 2024