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

1, 10, 110, 1320, 17160, 240240, 3603600, 57657600, 980179200, 17643225600, 335221286400, 6704425728000, 140792940288000, 3097444686336000, 71241227785728000, 1709789466857472000, 42744736671436800000, 1111363153457356800000, 30006805143348633600000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

The p=9 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=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

Links

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

Crossrefs

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

Cf. A130534, A163931, A173333, A245334.

Programs

Haskell

a049398 = (flip div 362880) . a000142 . (+ 9)
-- Reinhard Zumkeller, Aug 31 2014

Magma

[Factorial(n+9)/362880: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011

Mathematica

a[n_] := (n + 9)!/9!; Array[a, 20, 0] (* Amiram Eldar, Jan 15 2023 *)

PARI

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

Formula

E.g.f.: 1/(1-x)^10.

a(n) = A173333(n+9,9). - Reinhard Zumkeller, Feb 19 2010

a(n) = A245334(n+9,n) / 10. - Reinhard Zumkeller, Aug 31 2014

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=0} 1/a(n) = 362880*e - 986409.

Sum_{n>=0} (-1)^n/a(n) = 133497 - 362880/e. (End)