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A055775
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Floor(n^n/n!).
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16
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1, 1, 2, 4, 10, 26, 64, 163, 416, 1067, 2755, 7147, 18613, 48638, 127463, 334864, 881657, 2325750, 6145596, 16263866, 43099804, 114356611, 303761260, 807692034, 2149632061, 5726042115, 15264691107, 40722913454, 108713644516
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Stirling's approximation for n! suggests that this should be about e^n/sqrt(pi*2n). R. W. Gosper has noted that e^n/sqrt(pi*(2n+1/3)) is significantly better.
n^n/n! = A001142(n)/A001142(n-1), where A001142(n) is product{k=0 to n} C(n,k) (where C() is a binomial coefficient). - Leroy Quet, May 01 2004
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
Eric Weisstein's World of Mathematics, Stirling's Approximation for n!
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FORMULA
| a(n) =[A000312(n)/A000142(n)]
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EXAMPLE
| a(5)=26 since 5^5=3125, 5!=120, 3125/120=26.0416666...
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MATHEMATICA
| lst={}; Do[AppendTo[lst, Floor[n^n/n! ]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
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PROG
| (MAGMA) [Floor((n^n)/Factorial(n)): n in [0..30]]; // Vincenzo Librandi, Aug 22 2011
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CROSSREFS
| Cf. A073225, A094082.
Cf. A053042, A036679, A061711 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 15 2009]
Sequence in context: A183947 A154322 A090031 * A090032 A090377 A151278
Adjacent sequences: A055772 A055773 A055774 * A055776 A055777 A055778
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jul 12 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 13 2000
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