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A049388
a(n) = (n+7)!/7!.
26
1, 8, 72, 720, 7920, 95040, 1235520, 17297280, 259459200, 4151347200, 70572902400, 1270312243200, 24135932620800, 482718652416000, 10137091700736000, 223016017416192000, 5129368400572416000, 123104841613737984000, 3077621040343449600000, 80018147048929689600000
OFFSET
0,2
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
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)
MATHEMATICA
((Range[0, 20]+7)!)/7! (* Harvey P. Dale, Jul 31 2012 *)
PROG
(Magma) [Factorial(n+7)/5040: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011
(Haskell)
a049388 = (flip div 5040) . a000142 . (+ 7)
-- Reinhard Zumkeller, Aug 31 2014
(PARI) vector(20, n, n--; (n+7)!/7!) \\ G. C. Greubel, Aug 15 2018
KEYWORD
easy,nonn
STATUS
approved