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%I #13 May 12 2020 16:24:17
%S 1,4,12,100,1085,1218,47201,556088,10659753,7281020,62927202701,
%T 7217988,60718623181177,595952851172,13324959230295,247016251998448,
%U 28505095507110827053,549689328228186,320305941258100632731917
%N Numerator of Sum_{k=1..n} n^k/k!.
%C n divides a(n) and a(n)/n = A119029(n). - _Alexander Adamchuk_, Oct 08 2006
%C Apparently, the three sequences T_1(n) = Sum_{k=1..n} n^(k-1)/k!, T_2(n) = Sum_{k=0..n} n^k/k!, and T_3(n) = Sum_{k=1..n} n^k/k!, with numerators in A119029, A120266, and A120267, respectively, have the same denominators, listed in A214401. This, however, is not immediately obvious. - _Petros Hadjicostas_, May 12 2020
%F a(n) = numerator(Sum_{k=1..n} n^k/k!).
%F a(n) = n*A119029(n). - _Alexander Adamchuk_, Oct 08 2006
%e The first few fractions are 1, 4, 12, 100/3, 1085/12, 1218/5, 47201/72, 556088/315, 10659753/2240, 7281020/567, ... = A120267/A214401. - _Petros Hadjicostas_, May 12 2020
%t Numerator[Table[Sum[n^k/k!, {k,1,n}], {n,1,30}]]
%Y Cf. A063170, A090878, A093101, A119029, A120266, A214401 (denominators), A214402.
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Jun 30 2006
%E Various sections edited by _Petros Hadjicostas_, May 12 2020~