A049389 a(n) = (n+8)!/8!.

1, 9, 90, 990, 11880, 154440, 2162160, 32432400, 518918400, 8821612800, 158789030400, 3016991577600, 60339831552000, 1267136462592000, 27877002177024000, 641171050071552000, 15388105201717248000, 384702630042931200000, 10002268381116211200000

Offset

0,2

Comments

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

Links

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

Formula

a(n)= A051380(n, 0)*(-1)^n (first unsigned column of triangle).

a(n) = (n+8)!/8!.

E.g.f.: 1/(1-x)^9.

a(n) = A173333(n+8,8). - Reinhard Zumkeller, Feb 19 2010

a(n) = A245334(n+8,n) / 9. - Reinhard Zumkeller, Aug 31 2014

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=0} 1/a(n) = 40320*e - 109600.

Sum_{n>=0} (-1)^n/a(n) = 40320/e - 14832. (End)

Mathematica

a[n_] := (n + 8)!/8!; Array[a, 20, 0] (* Amiram Eldar, Jan 15 2023 *)

Prog

(Magma) [Factorial(n+8)/40320: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011
(PARI) a(n) = (n+8)!/8!;
(Haskell)
a049389 = (flip div 40320) . a000142 . (+ 8)
-- Reinhard Zumkeller, Aug 31 2014

Crossrefs

Cf. A000142, A001710, A001715, A001720, A001725, A001730, A049388, A051379, A051380.

Cf. A130534, A163931, A173333, A245334.

Sequence in context: A165324 A082367 A276506 * A127769 A276961 A062815

Adjacent sequences: A049386 A049387 A049388 * A049390 A049391 A049392

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved