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Search: id:A090878
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| A090878 |
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Numerator of integral_{0..infinity} exp(-x)*(1+x/n)^n dx. |
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+0
5
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| 2, 5, 26, 103, 2194, 1223, 472730, 556403, 21323986, 7281587, 125858034202, 180451625, 121437725363954, 595953719897, 26649932810926, 3211211914492699, 285050975993898158530, 549689343118061, 640611888918574971191834
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also numerators of e_n(n) where e_n(x) is the exponential sum function exp_n(x) and where denominators are given by either A095996 (largest divisor of n! that is coprime to n) or A036503 (denominator of n^(n-2)/n!). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Nov 14 2005
a(n) is a multiple of A120266[n] or equals A120266[n], A120266[n] is numerator of Sum[n^k/k!,{k,0,n}], the integral = (n-1)!/n^(n-1) * the Sum. - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Apr 17 2008
The integral = (1/n^n)*A063170[n] (Schenker sums with n-th term, Integral_{0..infty} exp(-x)*(n+x)^n dx). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Apr 17 2008
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LINKS
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Eric Weisstein. "Exponential Sum Function".
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FORMULA
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a(n) = A036505(n-1)*Sum(A128433(n)/A128434(n): 0<=k<=n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 03 2007
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MATHEMATICA
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f[n_] := Integrate[E^(-x)*(1 + x/n)^n, {x, 0, Infinity}]; Table[ Numerator[ f[n]], {n, 1, 20}]
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CROSSREFS
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Denominators in A036505.
Cf. A120266, A063170.
Sequence in context: A160048 A019047 A045903 this_sequence A120762 A072268 A019014
Adjacent sequences: A090875 A090876 A090877 this_sequence A090879 A090880 A090881
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KEYWORD
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nonn,frac
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 13 2004
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EXTENSIONS
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Definition corrected by Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Apr 17 2008
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