A282822 a(n) = (n - 4)*n! for n>=0.

-4, -3, -4, -6, 0, 120, 1440, 15120, 161280, 1814400, 21772800, 279417600, 3832012800, 56043187200, 871782912000, 14384418048000, 251073478656000, 4623936565248000, 89633231880192000, 1824676506132480000, 38926432130826240000, 868546016919060480000

Offset: 0

Author

Bruno Berselli, Feb 22 2017

Keywords

• sign
• easy

Crossrefs

Cf. A034865.

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

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

Programs

Mathematica

Table[(n - 4) n!, {n, 0, 30}] (* or *)
RecurrenceTable[{a[0] == -4, a[n] == n a[n - 1] + n!}, a, {n, 0, 30}]

Formula

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

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

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

From Amiram Eldar, Jan 14 2021: (Start)

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.

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)