A372747 - OEIS

%I #7 May 12 2024 10:04:16

%S 0,1,1,4,28,270,3185,42830,636250,10765885,227860725,6003043950,

%T 152451368175,2205648850800,1614364541325,6690753945813375,

%U 787760273195291625,-6787610390670062625,-7103289749314032719250,-59946385622086525694250,117473730537013548978420000

%N E.g.f. A(x) satisfies A(A(A(A(A(x))))) = (-1/5) * log(1 - 5*x).

%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) * |Stirling1(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. A220112, A372698.

%K sign

%O 0,4

%A _Seiichi Manyama_, May 12 2024