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A217033 Expansion of e.g.f. 1/(1 - log(1 - log(1-x))).

%I A217033 #20 May 11 2023 10:26:38
%S A217033 1,1,2,7,33,198,1432,12136,117772,1287718,15658052,209568126,
%T A217033 3061140398,48454548452,826155841924,15094511153752,294206836405288,
%U A217033 6093273074402848,133628182522968752,3093469935389714928,75384936371166307872,1928960833317580172688
%N A217033 Expansion of e.g.f. 1/(1 - log(1 - log(1-x))).
%H A217033 Vincenzo Librandi, <a href="/A217033/b217033.txt">Table of n, a(n) for n = 0..200</a>
%F A217033 a(n) ~ n! * exp(2-exp(1))/(1-exp(1-exp(1)))^(n+1). - _Vaclav Kotesovec_, Feb 12 2013
%F A217033 a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A006252(k). - _Seiichi Manyama_, May 11 2023
%e A217033 E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 33*x^4/4! + 198*x^5/5! +...
%t A217033 CoefficientList[Series[1/(1-Log[1-Log[1-x]]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Feb 12 2013 *)
%o A217033 (PARI) {a(n)=n!*polcoeff(1/(1-log(1-log(1-x +x*O(x^n)))),n)}
%o A217033 for(n=0,25,print1(a(n),", "))
%Y A217033 Cf. A089064, A305323.
%K A217033 nonn
%O A217033 0,3
%A A217033 _Paul D. Hanna_, Sep 24 2012