Search: id:A090878
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%I A090878
%S A090878 2,5,26,103,2194,1223,472730,556403,21323986,7281587,125858034202,
%T A090878 180451625,121437725363954,595953719897,26649932810926,3211211914492699,
%U A090878 285050975993898158530,549689343118061,640611888918574971191834
%N A090878 Numerator of integral_{0..infinity} exp(-x)*(1+x/n)^n dx.
%C A090878 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
%C A090878 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
%C A090878 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
%H A090878 Eric Weisstein. <a href="http://mathworld.wolfram.com/ExponentialSumFunction.html">
               "Exponential Sum Function"</a>.
%F A090878 a(n) = A036505(n-1)*Sum(A128433(n)/A128434(n): 0<=k<=n). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Mar 03 2007
%t A090878 f[n_] := Integrate[E^(-x)*(1 + x/n)^n, {x, 0, Infinity}]; Table[ Numerator[ 
               f[n]], {n, 1, 20}]
%Y A090878 Denominators in A036505.
%Y A090878 Cf. A120266, A063170.
%Y A090878 Sequence in context: A160048 A019047 A045903 this_sequence A120762 A072268 
               A019014
%Y A090878 Adjacent sequences: A090875 A090876 A090877 this_sequence A090879 A090880 
               A090881
%K A090878 nonn,frac
%O A090878 1,1
%A A090878 Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 13 2004
%E A090878 Definition corrected by Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), 
               Apr 17 2008

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