login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

E.g.f. A(x) satisfies A(A(A(A(A(x))))) = x * exp(5*x).
2

%I #7 May 12 2024 10:04:26

%S 0,1,2,-9,124,-2555,64170,-1675205,34049800,291956985,-91405776050,

%T 5482374369175,-21606376112100,-22274239387748075,-291056718409548350,

%U 568116108097921207875,-49271691434180884982000,-12837851845468554658031375

%N E.g.f. A(x) satisfies A(A(A(A(A(x))))) = x * exp(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*m)^(n-m) * binomial(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. A199852, A372736, A372737.

%K sign

%O 0,3

%A _Seiichi Manyama_, May 12 2024