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%I #12 May 05 2024 08:54:52
%S 0,1,1,1,-24,176,-524,-5124,87126,-506774,-1759824,57671226,
%T -358791624,-2206347624,49453238976,-92944954824,-4824317301399,
%U 31062072140001,557647434392001,-6058153265478399,-93734220877891074,1402372000511972226,21436083233577492876
%N G.f. A(x) satisfies A(A(A(A(A(x))))) = x + 5*x^2 + 25*x^3.
%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) * Sum_{l=0..m} binomial(l,n-3*m+2*l) * binomial(m,l) - 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. A220110, A220288, A371841, A372537.
%K sign
%O 0,5
%A _Seiichi Manyama_, May 04 2024