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 A282822 #16 Jan 14 2021 04:43:52
%S A282822 -4,-3,-4,-6,0,120,1440,15120,161280,1814400,21772800,279417600,
%T A282822 3832012800,56043187200,871782912000,14384418048000,251073478656000,
%U A282822 4623936565248000,89633231880192000,1824676506132480000,38926432130826240000,868546016919060480000
%N A282822 a(n) = (n - 4)*n! for n>=0.
%F A282822 E.g.f.: -(4 - 5*x)/(1 - x)^2.
%F A282822 a(n) = n*a(n-1) + n!, with n>0, a(0)=-4.
%F A282822 a(n) = 2*A034865(n) for n>3.
%F A282822 From _Amiram Eldar_, Jan 14 2021: (Start)
%F A282822 Sum_{n>=5} 1/a(n) = 313/288 - 5*e/12 - gamma/24 + Ei(1)/24 = 313/288 - (5/12)*A001113 - (1/24)*A001620 + A091725/24.
%F A282822 Sum_{n>=5} (-1)^(n+1)/a(n) = -25/288 + 1/(6*e) + gamma/24 - Ei(-1)/24 = -25/288 - (1/6)*A068985 + (1/24)*A001620 + (1/24)*A099285. (End)
%t A282822 Table[(n - 4) n!, {n, 0, 30}] (* or *)
%t A282822 RecurrenceTable[{a[0] == -4, a[n] == n a[n - 1] + n!}, a, {n, 0, 30}]
%Y A282822 Cf. A034865.
%Y A282822 Cf. sequences with formula (n + k)*n! listed in A282466.
%Y A282822 Cf. A001113, A001620, A068985, A091725, A099285.
%K A282822 sign,easy
%O A282822 0,1
%A A282822 _Bruno Berselli_, Feb 22 2017