A158874 a(n) = (n + 4)*(n + 3)*(n + 2)*(n + 1)*n / 5 = 24*A000389(n+4).

0, 24, 144, 504, 1344, 3024, 6048, 11088, 19008, 30888, 48048, 72072, 104832, 148512, 205632, 279072, 372096, 488376, 632016, 807576, 1020096, 1275120, 1578720, 1937520, 2358720, 2850120, 3420144, 4077864, 4833024, 5696064, 6678144, 7791168, 9047808

Offset: 0

Author

N. J. A. Sloane, Nov 29 2009

Keywords

• nonn
• easy

References

• L. B. W. Jolley, Summation of Series, Dover, 1961, eq. (48), page 8.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Partial sums of A052762.

Programs

Magma

[n*(n^4+10*n^3+35*n^2+50*n+24)/5: n in [0..30]]; // Vincenzo Librandi, Oct 05 2011

Mathematica

Table[(n + 4)*(n + 3)*(n + 2)*(n + 1)*n/5, {n,0,50}] (* G. C. Greubel, Nov 21 2017 *)

PARI

for(n=0,30, print1((n + 4)*(n + 3)*(n + 2)*(n + 1)*n/5, ", ")) \\ G. C. Greubel, Nov 21 2017

Formula

G.f.: 24*x / (x-1)^6 . - R. J. Mathar, Oct 03 2011

E.g.f.: x*(x^4 + 20*x^3 + 120*x^2 + 240*x + 120)*exp(x)/5. - G. C. Greubel, Nov 21 2017

From Amiram Eldar, Jul 02 2023: (Start)

Sum_{n>=1} 1/a(n) = 5/96.

Sum_{n>=1} (-1)^(n+1)/a(n) = 10*log(2)/3 - 655/288. (End)