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A049398 a(n) = (n+9)!/9!. 16
1, 10, 110, 1320, 17160, 240240, 3603600, 57657600, 980179200, 17643225600, 335221286400, 6704425728000, 140792940288000, 3097444686336000, 71241227785728000, 1709789466857472000, 42744736671436800000, 1111363153457356800000, 30006805143348633600000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
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)
MATHEMATICA
a[n_] := (n + 9)!/9!; Array[a, 20, 0] (* Amiram Eldar, Jan 15 2023 *)
PROG
(Magma) [Factorial(n+9)/362880: n in [0..25]]; // Vincenzo Librandi, Jul 20 2011
(PARI) a(n) = (n+9)!/9!
(Haskell)
a049398 = (flip div 362880) . a000142 . (+ 9)
-- Reinhard Zumkeller, Aug 31 2014
CROSSREFS
Sequence in context: A289414 A143749 A276507 * A055530 A108487 A099883
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)