A282466 a(n) = n*a(n-1) + n!, with n>0, a(0)=5.

5, 6, 14, 48, 216, 1200, 7920, 60480, 524160, 5080320, 54432000, 638668800, 8143027200, 112086374400, 1656387532800, 26153487360000, 439378587648000, 7825123418112000, 147254595231744000, 2919482409811968000, 60822550204416000000, 1328364496464445440000

Offset: 0

Author

Bruno Berselli, Feb 22 2017

Keywords

• nonn
• easy

References

• C. Mariconda and A. Tonolo, Calcolo discreto, Apogeo (2012), page 240 (Example 9.57 gives the recurrence).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A229039.

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).

Programs

Magma

A282466:= func< n | (n+5)*Factorial(n) >; // G. C. Greubel, May 14 2025

Mathematica

RecurrenceTable[{a[0] == 5, a[n] == n a[n - 1] + n!}, a, {n, 0, 30}] (* or *)
Table[(n + 5) n!, {n, 0, 30}]

SageMath

def A282466(n): return (n+5)*factorial(n) # G. C. Greubel, May 14 2025

Formula

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

a(n) = (n + 5)*n!.

a(n) = 2*A229039(n) for n>0.

From Amiram Eldar, Nov 06 2020: (Start)

Sum_{n>=0} 1/a(n) = 9*e - 24.

Sum_{n>=0} (-1)^n/a(n) = 24 - 65/e. (End)