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 A059099 #32 Jul 02 2025 16:02:00
%S A059099 1,2,7,33,198,1453,12669,128320,1482721,19260421,277913552,4410640919,
%T A059099 76360030701,1432144732762,28926138244883,625974400305541,
%U A059099 14449445989893990,354384475357492593,9202837263156670345,252260867710562944224,7278710072406887897461
%N A059099 Expansion of exp(exp(x)-1)/(2-exp(x)).
%C A059099 Row sums of A227343. - _Peter Bala_, Jul 11 2013
%C A059099 The sequence gives the number of barred preferential arrangements of an n-set having one bar, where one fixed section is a free section and elements which are to go into the other section are partitioned into unordered nonempty subsets. - _Sithembele Nkonkobe_, Jul 02 2015
%H A059099 Zhanar Berikkyzy, Pamela E. Harris, Anna Pun, Catherine Yan, and Chenchen Zhao, <a href="https://arxiv.org/abs/2308.14183">Combinatorial Identities for Vacillating Tableaux</a>, arXiv:2308.14183 [math.CO], 2023. See pp. 12, 19, 29.
%H A059099 S. Nkonkobe and V. Murali, <a href="http://arxiv.org/abs/1503.06172">A study of a family of generating functions of Nelsen-Schmidt type and some identities on restricted barred preferential arrangements</a>, arXiv:1503.06172 [math.CO], 2015.
%F A059099 a(n) = Sum_{m=0..n} Sum_{i=0..n} Stirling2(n, i)*Product_{j=1..m} (i-j+1).
%F A059099 Stirling transform of A000522. - _Vladeta Jovovic_, May 10 2004
%F A059099 a(n) ~ n!*exp(1)/(2*(log(2))^(n+1)). - _Vaclav Kotesovec_, Jul 02 2015
%e A059099 exp(exp(x)-1)/(2-exp(x)) = 1 + 2*x + 7/2*x^2 + 11/2*x^3 + 33/4*x^4 + 1453/120*x^5 + 4223/240*x^6 + 1604/63*x^7 + ...
%p A059099 s := series(exp(exp(x)-1)/(2-exp(x)), x, 60): for i from 0 to 50 do printf(`%d,`,i!*coeff(s,x,i)) od:
%t A059099 CoefficientList[Series[E^(E^x-1)/(2-E^x), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jul 02 2015 *)
%Y A059099 Row sums of A059098.
%Y A059099 Cf. A001861, A000110, A005493, A049020, A227343.
%K A059099 easy,nonn
%O A059099 0,2
%A A059099 _Vladeta Jovovic_, Jan 02 2001
%E A059099 More terms from _James Sellers_, Jan 03 2001