A282822 - OEIS

%I #16 Jan 14 2021 04:43:52

%S -4,-3,-4,-6,0,120,1440,15120,161280,1814400,21772800,279417600,

%T 3832012800,56043187200,871782912000,14384418048000,251073478656000,

%U 4623936565248000,89633231880192000,1824676506132480000,38926432130826240000,868546016919060480000

%N a(n) = (n - 4)*n! for n>=0.

%F E.g.f.: -(4 - 5*x)/(1 - x)^2.

%F a(n) = n*a(n-1) + n!, with n>0, a(0)=-4.

%F a(n) = 2*A034865(n) for n>3.

%F From _Amiram Eldar_, Jan 14 2021: (Start)

%F 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 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 Table[(n - 4) n!, {n, 0, 30}] (* or *)

%t RecurrenceTable[{a[0] == -4, a[n] == n a[n - 1] + n!}, a, {n, 0, 30}]

%Y Cf. A034865.

%Y Cf. sequences with formula (n + k)*n! listed in A282466.

%Y Cf. A001113, A001620, A068985, A091725, A099285.

%K sign,easy

%O 0,1

%A _Bruno Berselli_, Feb 22 2017