A143217 a(n) = n! * (!(n+1)) = n! * Sum_{k=0..n} k!.

1, 2, 8, 60, 816, 18480, 629280, 29806560, 1864154880, 148459288320, 14652782323200, 1754531527795200, 250496911136102400, 42032247888401971200, 8188505926989625036800, 1832839841629043799552000, 467088574163459753336832000, 134454052266325985991942144000

Offset: 0

Author

Gary W. Adamson, Jul 30 2008

Keywords

• nonn
• easy

Examples

			a(4) = 816 = 4! * 34, where 34 = A003422(4) and A000142 = (1, 1, 2, 6, 24, 120, ...).
a(4) = 816 = sum of row 4 terms of triangle A143216: (24 + 24 + 48 + 144 + 576).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A000142, A003422, A061640.

Cf. A143216, A217238, A217239.

Programs

Magma

[Factorial(n)*(&+[Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jul 12 2022

Mathematica

Table[n!*Sum[i!, {i, 0, n}], {n, 0, 16}]

SageMath

f=factorial; [f(n)*sum(f(k) for k in (0..n)) for n in (0..40)] # G. C. Greubel, Jul 12 2022

Formula

a(n) = A000142(n) * A003422(n+1), where A000142 = the factorials and A003422 = partial sums of the factorials. [Corrected by Georg Fischer, Dec 13 2022]

Equals row sums of triangle A143216.

Extensions

Edited and extended by Olivier Gérard, Sep 28 2012