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%I #12 May 05 2024 10:41:57
%S 0,1,10,-25,1000,-18125,131250,11609375,-630156250,4314062500,
%T 1173535156250,-38006699218750,-4262573730468750,321379049072265625,
%U 20787043081054687500,-3209395283374023437500,-116229452332824707031250,39638105812041778564453125
%N G.f. A(x) satisfies A(A(A(A(A(x))))) = Sum_{k>=1} k * 25^(k-1) * x^k.
%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 * ( 25^(n-m) * binomial(n+m-1,2*m-1) - 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. A309509, A372492, A372499, A372522.
%Y Cf. A141120.
%K sign
%O 0,3
%A _Seiichi Manyama_, May 04 2024
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