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%I #29 Oct 23 2023 10:03:30
%S 1,4,40,720,20160,806400,43545600,3048192000,268240896000,
%T 28970016768000,3766102179840000,579979735695360000,
%U 104396352425164800000,21714441304434278400000,5168037030455358259200000,1395369998222946729984000000,424192479459775805915136000000
%N a(n) = n!*(n+3)! / 3!.
%H Vincenzo Librandi, <a href="/A010792/b010792.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F From _Amiram Eldar_, Sep 27 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 6*BesselI(3,2) = 6*A261879.
%F Sum_{n>=0} (-1)^n/a(n) = 6*BesselJ(3,2). (End)
%p f := n->n!*(n+3)!/3!;
%t Table[n! (n + 3)! / 3!, {n, 0, 20}] (* _Vincenzo Librandi_, Feb 25 2017 *)
%o (Magma) [Factorial(n)*Factorial(n+3)/6: n in [0..20]]; // _Vincenzo Librandi_, Feb 25 2017
%o (PARI) a(n) = n!^2*binomial(n+3,3) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y Cf. A010791, A010793, A010794, A010795, A261879.
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Feb 25 2017
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