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 A222059 #20 Jun 03 2022 07:38:24
%S A222059 0,1,5,44,590,11094,276924,8821056,347992560,16608856176,941180477760,
%T A222059 62356907861280,4768658639919360,416372600735314560,
%U A222059 41123273761815517440,4557176483095745510400,562635159090115071744000,76906191809174747446425600,11573912988161070649533849600
%N A222059 a(n) = n-th harmonic-exponential number, multiplied by n!.
%H A222059 Ayhan Dil and Veli Kurt, <a href="http://www.emis.de/journals/INTEGERS/papers/m38/m38.Abstract.html">Polynomials related to harmonic numbers and evaluation of harmonic number series I</a>, INTEGERS, 12 (2012), #A38. See Eq. (60).
%F A222059 a(n) = Sum_{k=0..n} A008277(n,k) * (A001008(k)/A002805(k)) * A000142(n). - _Michel Marcus_, Feb 08 2013
%F A222059 Sum_{n>=0} a(n) * x^n / n!^2 = Sum_{n>=1} H(n) * (exp(x) - 1)^n / n!, where H(n) is the n-th harmonic number. - _Ilya Gutkovskiy_, Jun 03 2022
%t A222059 Table[Sum[HarmonicNumber[k] StirlingS2[n, k] n!, {k, 0, n}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 20 2015 *)
%o A222059 (PARI) a(n) = sum(k=0, n, (sum(i=0, k, (-1)^i*binomial(k, i)*i^n) * (-1)^k/k!)*sum(i=1, k, 1/i) * n!); \\ _Michel Marcus_, Feb 08 2013
%Y A222059 Cf. A001008, A002805, A008277, A222058.
%K A222059 nonn
%O A222059 0,3
%A A222059 _N. J. A. Sloane_, Feb 08 2013
%E A222059 More terms from _Michel Marcus_, Feb 08 2013