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A363009 Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(exp(x) - 1) - 1) - 1) - 1)).

%I A363009 #12 May 12 2023 15:07:29
%S A363009 1,1,7,71,949,15775,313920,7279795,192828745,5744627550,190131836270,
%T A363009 6921735519110,274885665920198,11826225289547024,547926995688877245,
%U A363009 27199542114163170649,1440220170795372833970,81026116511855753816058
%N A363009 Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(exp(x) - 1) - 1) - 1) - 1)).
%H A363009 Alois P. Heinz, <a href="/A363009/b363009.txt">Table of n, a(n) for n = 0..375</a>
%F A363009 a(n) = T(n,5), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = n!.
%p A363009 b:= proc(n, m, t) option remember; `if`(n=0, `if`(t=1, m!,
%p A363009       b(m, 0, t-1)), m*b(n-1, m, t)+b(n-1, m+1, t))
%p A363009     end:
%p A363009 a:= n-> b(n, 0, 5):
%p A363009 seq(a(n), n=0..20);  # _Alois P. Heinz_, May 12 2023
%o A363009 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(exp(exp(exp(exp(x)-1)-1)-1)-1))))
%Y A363009 Row p=5 of A153278 (for n>=1).
%Y A363009 Column k=5 of A363007.
%Y A363009 Cf. A351428.
%K A363009 nonn
%O A363009 0,3
%A A363009 _Seiichi Manyama_, May 12 2023