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

1, 11, 132, 1716, 24024, 360360, 5765760, 98017920, 1764322560, 33522128640, 670442572800, 14079294028800, 309744468633600, 7124122778572800, 170978946685747200, 4274473667143680000, 111136315345735680000, 3000680514334863360000, 84019054401376174080000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

The p=10 member of the p-family of sequences {(n+p-1)!/p!}, n >= 1.

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000142, A001710, A001715, A001720, A001725, A001730, A049388, A049389, A049398.

Cf. A130534, A163931, A173333, A245334.

Programs

Haskell

a051431 = (flip div 3628800) . a000142 . (+ 10)
-- Reinhard Zumkeller, Aug 31 2014

Magma

[Factorial(n+10)/3628800: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011

Mathematica

a[n_] := (n + 10)!/10!; Array[a, 20, 0] (* Amiram Eldar, Jan 15 2023 *)

Formula

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

E.g.f.: 1/(1-x)^11.

a(n) = A173333(n+10,10). - Reinhard Zumkeller, Feb 19 2010

a(n) = A245334(n+10,n) / 11. - Reinhard Zumkeller, Aug 31 2014

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=0} 1/a(n) = 3628800*e - 9864100.

Sum_{n>=0} (-1)^n/a(n) = 3628800/e - 1334960. (End)