This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A214401 #31 Feb 16 2025 08:33:18
%S A214401 1,1,1,3,12,5,72,315,2240,567,1814400,77,239500800,868725,7175168,
%T A214401 49116375,2092278988800,14889875,3201186852864000,14849255421,
%U A214401 3783802880000,3543572316375,562000363888803840000,2505147019375,496358721386591551488
%N A214401 Denominator of Sum_{k=0..n} n^k/k!.
%C A214401 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 the current sequence. This, however, is not immediately obvious. - _Petros Hadjicostas_, May 12 2020
%H A214401 Michel Marcus, <a href="/A214401/b214401.txt">Table of n, a(n) for n = 1..150</a>
%H A214401 Eric Weisstein, <a href="https://mathworld.wolfram.com/ExponentialSumFunction.html">Exponential Sum Function</a>.
%F A214401 a(n) = n!/A214402(n).
%t A214401 Denominator[Table[Sum[n^k/k!, {k, 0, n}], {n, 1, 30}]]
%o A214401 (PARI) a(n) = denominator(sum(k=0, n, n^k/k!)); \\ _Michel Marcus_, Apr 20 2021
%Y A214401 Numerators are A120266.
%Y A214401 Cf. also A063170, A090878, A093101, A119029, A120267, A214402.
%K A214401 frac,nonn
%O A214401 1,4
%A A214401 _Jonathan Sondow_, Jul 15 2012