%I #31 Oct 16 2023 10:03:09

%S 1,2,7,33,198,1453,12669,128320,1482721,19260421,277913552,4410640919,

%T 76360030701,1432144732762,28926138244883,625974400305541,

%U 14449445989893990,354384475357492593,9202837263156670345,252260867710562944224,7278710072406887897461

%N Expansion of exp(exp(x)-1)/(2-exp(x)).

%C Row sums of A227343. - _Peter Bala_, Jul 11 2013

%C 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 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 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 a(n) = Sum_{m=0..n} Sum_{i=0..n} Stirling2(n, i)*Product_{j=1..m} (i-j+1).

%F Stirling transform of A000522. - _Vladeta Jovovic_, May 10 2004

%F a(n) ~ n!*exp(1)/(2*(log(2))^(n+1)). - _Vaclav Kotesovec_, Jul 02 2015

%e 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 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 CoefficientList[Series[E^(E^x-1)/(2-E^x), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jul 02 2015 *)

%Y Row sums of A059098.

%Y Cf. A001861, A000110, A005493, A049020, A227343.

%K easy,nonn

%O 0,2

%A _Vladeta Jovovic_, Jan 02 2001

%E More terms from _James A. Sellers_, Jan 03 2001