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A363008 Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(x) - 1) - 1) - 1)).

%I A363008 #12 May 12 2023 15:03:50
%S A363008 1,1,6,52,594,8444,143783,2854261,64735570,1651560175,46814933977,
%T A363008 1459689346911,49650414218071,1829560770160335,72603137881845927,
%U A363008 3086932915850946633,139999909097319319787,6746170002325663539844,344199636595620793896784
%N A363008 Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(x) - 1) - 1) - 1)).
%H A363008 Alois P. Heinz, <a href="/A363008/b363008.txt">Table of n, a(n) for n = 0..383</a>
%F A363008 a(n) = T(n,4), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = n!.
%p A363008 b:= proc(n, m, t) option remember; `if`(n=0, `if`(t=1, m!,
%p A363008       b(m, 0, t-1)), m*b(n-1, m, t)+b(n-1, m+1, t))
%p A363008     end:
%p A363008 a:= n-> b(n, 0, 4):
%p A363008 seq(a(n), n=0..20);  # _Alois P. Heinz_, May 12 2023
%o A363008 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(exp(exp(exp(x)-1)-1)-1))))
%Y A363008 Row p=4 of A153278 (for n>=1).
%Y A363008 Column k=4 of A363007.
%Y A363008 Cf. A351427.
%K A363008 nonn
%O A363008 0,3
%A A363008 _Seiichi Manyama_, May 12 2023