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A010792 a(n) = n!*(n+3)! / 3!.

%I A010792 #34 Jul 08 2025 01:45:56
%S A010792 1,4,40,720,20160,806400,43545600,3048192000,268240896000,
%T A010792 28970016768000,3766102179840000,579979735695360000,
%U A010792 104396352425164800000,21714441304434278400000,5168037030455358259200000,1395369998222946729984000000,424192479459775805915136000000
%N A010792 a(n) = n!*(n+3)! / 3!.
%H A010792 Vincenzo Librandi, <a href="/A010792/b010792.txt">Table of n, a(n) for n = 0..200</a>
%H A010792 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A010792 From _Amiram Eldar_, Sep 27 2022: (Start)
%F A010792 Sum_{n>=0} 1/a(n) = 6*BesselI(3,2) = 6*A261879.
%F A010792 Sum_{n>=0} (-1)^n/a(n) = 6*BesselJ(3,2). (End)
%F A010792 a(n) = 1/([x^n] hypergeom([], [4], x)). - _Peter Luschny_, Sep 13 2024
%p A010792 f := n->n!*(n+3)!/3!;
%t A010792 Table[n! (n + 3)! / 3!, {n, 0, 20}] (* _Vincenzo Librandi_, Feb 25 2017 *)
%o A010792 (Magma) [Factorial(n)*Factorial(n+3)/6: n in [0..20]]; // _Vincenzo Librandi_, Feb 25 2017
%o A010792 (PARI) a(n) = n!^2*binomial(n+3,3) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y A010792 Cf. A010791, A010793, A010794, A010795, A261879.
%K A010792 nonn
%O A010792 0,2
%A A010792 _N. J. A. Sloane_
%E A010792 More terms from _Vincenzo Librandi_, Feb 25 2017