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%I #6 May 12 2024 10:04:20
%S 0,1,1,-1,3,-5,-140,3265,-35145,-423300,29156450,-244674300,
%T -35711239900,1323533263450,79091925545150,-7803803198306500,
%U -249393437031632750,68360119098495114000,386044168785212367500,-899401682046014451577000
%N E.g.f. A(x) satisfies A(A(A(A(A(x))))) = (exp(5*x) - 1)/5.
%F Define the sequence b(n,m) as follows. If n<m, b(n,m) = 0, else if n=m, b(n,m) = 1, otherwise b(n,m) = 1/5 * ( 5^(n-m) * Stirling2(n,m) - Sum_{l=m+1..n-1} (b(n,l) + Sum_{k=l..n} (b(n,k) + Sum_{j=k..n} (b(n,j) + Sum_{i=j..n} b(n,i) * b(i,j)) * b(j,k)) * b(k,l)) * b(l,m) ). a(n) = b(n,1).
%Y Cf. A184011, A209519.
%K sign
%O 0,5
%A _Seiichi Manyama_, May 12 2024
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