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%I #30 Feb 05 2022 16:54:55
%S 0,1,4,16,68,311,1530,8065,45344,270724,1709526,11376135,79520644,
%T 582207393,4453142140,35500884556,294365897104,2533900264547,
%U 22604669612078,208656457858161,1990060882027600
%N Expansion of (1/2)*(exp(2*x)-1)*exp(exp(x)-1).
%C Starting (1, 4, 16, 68, 311, ...), = A008277 * A000217, i.e., the product of the Stirling2 triangle and triangular series. - _Gary W. Adamson_, Jan 31 2008
%H Vincenzo Librandi, <a href="/A059606/b059606.txt">Table of n, a(n) for n = 0..200</a>
%H Vladeta Jovovic, <a href="/A059604/a059604.pdf">More information</a>.
%F a(n) = Sum_{i=0..n} Stirling2(n, i)*binomial(i+1, 2).
%F a(n) = (1/2)*(Bell(n+2)-Bell(n+1)-Bell(n)). - _Vladeta Jovovic_, Sep 23 2003
%F G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^k/Product_{j=1..k} (1 - j*x). - _Ilya Gutkovskiy_, Jun 19 2018
%F a(n) ~ n^2 * Bell(n) / (2*LambertW(n)^2) * (1 - LambertW(n)/n). - _Vaclav Kotesovec_, Jul 28 2021
%p s := series(1/2*(exp(2*x)-1)*exp(exp(x)-1), x, 21): for i from 0 to 20 do printf(`%d,`,i!*coeff(s,x,i)) od:
%t With[{nn=20},CoefficientList[Series[((Exp[2x]-1)Exp[Exp[x]-1])/2,{x,0,nn}] ,x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 10 2011 *)
%Y Cf. A000110, A005493, A059604, A059605.
%Y Cf. A035098.
%Y Cf. A008277, A000217.
%K nonn,easy
%O 0,3
%A _Vladeta Jovovic_, Jan 29 2001
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