A049388 a(n) = (n+7)!/7!.

1, 8, 72, 720, 7920, 95040, 1235520, 17297280, 259459200, 4151347200, 70572902400, 1270312243200, 24135932620800, 482718652416000, 10137091700736000, 223016017416192000, 5129368400572416000, 123104841613737984000, 3077621040343449600000, 80018147048929689600000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

The asymptotic expansion of the higher order exponential integral E(x,m=1,n=8) ~ exp(-x)/x*(1 - 8/x + 72/x^2 - 720/x^3 + 7920/x^4 - 95040/x^5 + 235520/x^6 - 17297280/x^7 + ...) leads to the sequence given above. See A163931 and A130534 for more information. - Johannes W. Meijer, Oct 20 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000142, A001710, A001715, A001720, A001725, A001730, A051339, A051379.

Cf. A130534, A163931, A173333, A245334.

Programs

Haskell

a049388 = (flip div 5040) . a000142 . (+ 7)
-- Reinhard Zumkeller, Aug 31 2014

Magma

[Factorial(n+7)/5040: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011

Mathematica

((Range[0,20]+7)!)/7! (* Harvey P. Dale, Jul 31 2012 *)

PARI

vector(20,n,n--; (n+7)!/7!) \\ G. C. Greubel, Aug 15 2018

Formula

a(n)= A051379(n, 0)*(-1)^n (first unsigned column of triangle).

a(n) = (n+7)!/7!.

E.g.f.: 1/(1-x)^8.

a(n) = A173333(n+7,7). - Reinhard Zumkeller, Feb 19 2010

a(n) = A245334(n+7,n) / 8. - Reinhard Zumkeller, Aug 31 2014

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=0} 1/a(n) = 5040*e - 13699.

Sum_{n>=0} (-1)^n/a(n) = 1855 - 5040/e. (End)