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%I #30 Jan 15 2023 02:41:20
%S 1,8,72,720,7920,95040,1235520,17297280,259459200,4151347200,
%T 70572902400,1270312243200,24135932620800,482718652416000,
%U 10137091700736000,223016017416192000,5129368400572416000,123104841613737984000,3077621040343449600000,80018147048929689600000
%N a(n) = (n+7)!/7!.
%C 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
%H Vincenzo Librandi, <a href="/A049388/b049388.txt">Table of n, a(n) for n = 0..300</a>
%F a(n)= A051379(n, 0)*(-1)^n (first unsigned column of triangle).
%F a(n) = (n+7)!/7!.
%F E.g.f.: 1/(1-x)^8.
%F a(n) = A173333(n+7,7). - _Reinhard Zumkeller_, Feb 19 2010
%F a(n) = A245334(n+7,n) / 8. - _Reinhard Zumkeller_, Aug 31 2014
%F From _Amiram Eldar_, Jan 15 2023: (Start)
%F Sum_{n>=0} 1/a(n) = 5040*e - 13699.
%F Sum_{n>=0} (-1)^n/a(n) = 1855 - 5040/e. (End)
%t ((Range[0,20]+7)!)/7! (* _Harvey P. Dale_, Jul 31 2012 *)
%o (Magma) [Factorial(n+7)/5040: n in [0..25]]; // _Vincenzo Librandi_, Jul 20 2011
%o (Haskell)
%o a049388 = (flip div 5040) . a000142 . (+ 7)
%o -- _Reinhard Zumkeller_, Aug 31 2014
%o (PARI) vector(20,n,n--; (n+7)!/7!) \\ _G. C. Greubel_, Aug 15 2018
%Y Cf. A000142, A001710, A001715, A001720, A001725, A001730, A051339, A051379.
%Y Cf. A130534, A163931, A173333, A245334.
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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