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A049398 a(n) = (n+9)!/9!.

%I A049398 #24 Jan 15 2023 02:41:02
%S A049398 1,10,110,1320,17160,240240,3603600,57657600,980179200,17643225600,
%T A049398 335221286400,6704425728000,140792940288000,3097444686336000,
%U A049398 71241227785728000,1709789466857472000,42744736671436800000,1111363153457356800000,30006805143348633600000
%N A049398 a(n) = (n+9)!/9!.
%C A049398 The p=9 member of the p-family of sequences {(n+p-1)!/p!}, n >= 1.
%C A049398 The asymptotic expansion of the higher order exponential integral E(x,m=1,n=10) ~ exp(-x)/x*(1 - 10/x + 110/x^2 - 1320/x^3 + 17160/x^4 - 240240/x^5 + 3603600/x^6 - ...) leads to the sequence given above. See A163931 and A130534 for more information. - _Johannes W. Meijer_, Oct 20 2009
%H A049398 Vincenzo Librandi, <a href="/A049398/b049398.txt">Table of n, a(n) for n = 0..300</a>
%F A049398 E.g.f.: 1/(1-x)^10.
%F A049398 a(n) = A173333(n+9,9). - _Reinhard Zumkeller_, Feb 19 2010
%F A049398 a(n) = A245334(n+9,n) / 10. - _Reinhard Zumkeller_, Aug 31 2014
%F A049398 From _Amiram Eldar_, Jan 15 2023: (Start)
%F A049398 Sum_{n>=0} 1/a(n) = 362880*e - 986409.
%F A049398 Sum_{n>=0} (-1)^n/a(n) = 133497 - 362880/e. (End)
%t A049398 a[n_] := (n + 9)!/9!; Array[a, 20, 0] (* _Amiram Eldar_, Jan 15 2023 *)
%o A049398 (Magma) [Factorial(n+9)/362880: n in [0..25]]; // _Vincenzo Librandi_, Jul 20 2011
%o A049398 (PARI) a(n) = (n+9)!/9!
%o A049398 (Haskell)
%o A049398 a049398 = (flip div 362880) . a000142 . (+ 9)
%o A049398 -- _Reinhard Zumkeller_, Aug 31 2014
%Y A049398 Cf. A000142, A001710, A001715, A001720, A001725, A001730, A049388, A049389.
%Y A049398 Cf. A130534, A163931, A173333, A245334.
%K A049398 easy,nonn
%O A049398 0,2
%A A049398 _Wolfdieter Lang_