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A051431 a(n) = (n+10)!/10!.

%I A051431 #21 Jan 15 2023 02:40:46
%S A051431 1,11,132,1716,24024,360360,5765760,98017920,1764322560,33522128640,
%T A051431 670442572800,14079294028800,309744468633600,7124122778572800,
%U A051431 170978946685747200,4274473667143680000,111136315345735680000,3000680514334863360000,84019054401376174080000
%N A051431 a(n) = (n+10)!/10!.
%C A051431 The p=10 member of the p-family of sequences {(n+p-1)!/p!}, n >= 1.
%C A051431 The asymptotic expansion of the higher-order exponential integral E(x,m=1,n=11) ~ exp(-x)/x*(1 - 11/x + 132/x^2 - 1716/x^3 + 24024/x^4 - 360360/x^5 + 5765760/x^6 - ...) leads to the sequence given above. See A163931 and A130534 for more information. - _Johannes W. Meijer_, Oct 20 2009
%H A051431 Vincenzo Librandi, <a href="/A051431/b051431.txt">Table of n, a(n) for n = 0..300</a>
%F A051431 a(n) = (n+10)!/10!
%F A051431 E.g.f.: 1/(1-x)^11.
%F A051431 a(n) = A173333(n+10,10). - _Reinhard Zumkeller_, Feb 19 2010
%F A051431 a(n) = A245334(n+10,n) / 11. - _Reinhard Zumkeller_, Aug 31 2014
%F A051431 From _Amiram Eldar_, Jan 15 2023: (Start)
%F A051431 Sum_{n>=0} 1/a(n) = 3628800*e - 9864100.
%F A051431 Sum_{n>=0} (-1)^n/a(n) = 3628800/e - 1334960. (End)
%t A051431 a[n_] := (n + 10)!/10!; Array[a, 20, 0] (* _Amiram Eldar_, Jan 15 2023 *)
%o A051431 (Magma) [Factorial(n+10)/3628800: n in [0..25]]; // _Vincenzo Librandi_, Jul 20 2011
%o A051431 (Haskell)
%o A051431 a051431 = (flip div 3628800) . a000142 . (+ 10)
%o A051431 -- _Reinhard Zumkeller_, Aug 31 2014
%Y A051431 Cf. A000142, A001710, A001715, A001720, A001725, A001730, A049388, A049389, A049398.
%Y A051431 Cf. A130534, A163931, A173333, A245334.
%K A051431 easy,nonn
%O A051431 0,2
%A A051431 _Wolfdieter Lang_