This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282466 #26 May 16 2025 16:31:20
%S A282466 5,6,14,48,216,1200,7920,60480,524160,5080320,54432000,638668800,
%T A282466 8143027200,112086374400,1656387532800,26153487360000,439378587648000,
%U A282466 7825123418112000,147254595231744000,2919482409811968000,60822550204416000000,1328364496464445440000
%N A282466 a(n) = n*a(n-1) + n!, with n>0, a(0)=5.
%D A282466 C. Mariconda and A. Tonolo, Calcolo discreto, Apogeo (2012), page 240 (Example 9.57 gives the recurrence).
%H A282466 G. C. Greubel, <a href="/A282466/b282466.txt">Table of n, a(n) for n = 0..440</a>
%F A282466 E.g.f.: (5 - 4*x)/(1 - x)^2.
%F A282466 a(n) = (n + 5)*n!.
%F A282466 a(n) = 2*A229039(n) for n>0.
%F A282466 From _Amiram Eldar_, Nov 06 2020: (Start)
%F A282466 Sum_{n>=0} 1/a(n) = 9*e - 24.
%F A282466 Sum_{n>=0} (-1)^n/a(n) = 24 - 65/e. (End)
%t A282466 RecurrenceTable[{a[0] == 5, a[n] == n a[n - 1] + n!}, a, {n, 0, 30}] (* or *)
%t A282466 Table[(n + 5) n!, {n, 0, 30}]
%o A282466 (Magma)
%o A282466 A282466:= func< n | (n+5)*Factorial(n) >; // _G. C. Greubel_, May 14 2025
%o A282466 (SageMath)
%o A282466 def A282466(n): return (n+5)*factorial(n) # _G. C. Greubel_, May 14 2025
%Y A282466 Cf. A229039.
%Y A282466 Cf. sequences with formula (n + k)*n!: A052521 (k=-5), A282822 (k=-4), A052520 (k=-3), A052571 (k=-2), A062119 (k=-1), A001563 (k=0), A000142 (k=1), A001048 (k=2), A052572 (k=3), A052644 (k=4), this sequence (k=5).
%K A282466 nonn,easy
%O A282466 0,1
%A A282466 _Bruno Berselli_, Feb 22 2017