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A372745
E.g.f. A(x) satisfies A(A(A(A(A(x))))) = x * exp(5*x).
2
0, 1, 2, -9, 124, -2555, 64170, -1675205, 34049800, 291956985, -91405776050, 5482374369175, -21606376112100, -22274239387748075, -291056718409548350, 568116108097921207875, -49271691434180884982000, -12837851845468554658031375
OFFSET
0,3
FORMULA
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).
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 12 2024
STATUS
approved