|
%I #22 Jan 15 2023 02:41:41
%S 1,9,90,990,11880,154440,2162160,32432400,518918400,8821612800,
%T 158789030400,3016991577600,60339831552000,1267136462592000,
%U 27877002177024000,641171050071552000,15388105201717248000,384702630042931200000,10002268381116211200000
%N a(n) = (n+8)!/8!.
%C The asymptotic expansion of the higher-order exponential integral E(x,m=1,n=9) ~ exp(-x)/x*(1 - 9/x + 90/x^2 - 990/x^3 + 11880/x^4 - 154440/x^5 + ...) leads to the sequence given above. See A163931 and A130534 for more information. - _Johannes W. Meijer_, Oct 20 2009
%H Vincenzo Librandi, <a href="/A049389/b049389.txt">Table of n, a(n) for n = 0..300</a>
%F a(n)= A051380(n, 0)*(-1)^n (first unsigned column of triangle).
%F a(n) = (n+8)!/8!.
%F E.g.f.: 1/(1-x)^9.
%F a(n) = A173333(n+8,8). - _Reinhard Zumkeller_, Feb 19 2010
%F a(n) = A245334(n+8,n) / 9. - _Reinhard Zumkeller_, Aug 31 2014
%F From _Amiram Eldar_, Jan 15 2023: (Start)
%F Sum_{n>=0} 1/a(n) = 40320*e - 109600.
%F Sum_{n>=0} (-1)^n/a(n) = 40320/e - 14832. (End)
%t a[n_] := (n + 8)!/8!; Array[a, 20, 0] (* _Amiram Eldar_, Jan 15 2023 *)
%o (Magma) [Factorial(n+8)/40320: n in [0..25]]; // _Vincenzo Librandi_, Jul 20 2011
%o (PARI) a(n) = (n+8)!/8!;
%o (Haskell)
%o a049389 = (flip div 40320) . a000142 . (+ 8)
%o -- _Reinhard Zumkeller_, Aug 31 2014
%Y Cf. A000142, A001710, A001715, A001720, A001725, A001730, A049388, A051379, A051380.
%Y Cf. A130534, A163931, A173333, A245334.
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
|
