A372746 E.g.f. A(x) satisfies A(A(A(A(A(x))))) = (exp(5*x) - 1)/5.

0, 1, 1, -1, 3, -5, -140, 3265, -35145, -423300, 29156450, -244674300, -35711239900, 1323533263450, 79091925545150, -7803803198306500, -249393437031632750, 68360119098495114000, 386044168785212367500, -899401682046014451577000

Offset

0,5

Links

Table of n, a(n) for n=0..19.

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^(n-m) * Stirling2(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

Cf. A184011, A209519.

Sequence in context: A225672 A355803 A240125 * A108013 A087307 A280427

Adjacent sequences: A372743 A372744 A372745 * A372747 A372748 A372749

Keyword

sign

Author

Seiichi Manyama, May 12 2024

Status

approved