A217033 - OEIS

%I #20 May 11 2023 10:26:38

%S 1,1,2,7,33,198,1432,12136,117772,1287718,15658052,209568126,

%T 3061140398,48454548452,826155841924,15094511153752,294206836405288,

%U 6093273074402848,133628182522968752,3093469935389714928,75384936371166307872,1928960833317580172688

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

%H Vincenzo Librandi, <a href="/A217033/b217033.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ n! * exp(2-exp(1))/(1-exp(1-exp(1)))^(n+1). - _Vaclav Kotesovec_, Feb 12 2013

%F a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A006252(k). - _Seiichi Manyama_, May 11 2023

%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 33*x^4/4! + 198*x^5/5! +...

%t CoefficientList[Series[1/(1-Log[1-Log[1-x]]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Feb 12 2013 *)

%o (PARI) {a(n)=n!*polcoeff(1/(1-log(1-log(1-x +x*O(x^n)))),n)}

%o for(n=0,25,print1(a(n),", "))

%Y Cf. A089064, A305323.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 24 2012