A372747 E.g.f. A(x) satisfies A(A(A(A(A(x))))) = (-1/5) * log(1 - 5*x).

0, 1, 1, 4, 28, 270, 3185, 42830, 636250, 10765885, 227860725, 6003043950, 152451368175, 2205648850800, 1614364541325, 6690753945813375, 787760273195291625, -6787610390670062625, -7103289749314032719250, -59946385622086525694250, 117473730537013548978420000

Offset

0,4

Links

Table of n, a(n) for n=0..20.

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) * |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).

Crossrefs

Cf. A220112, A372698.

Sequence in context: A138272 A367470 A361049 * A245060 A191686 A231694

Adjacent sequences: A372744 A372745 A372746 * A372748 A372749 A372750

Keyword

sign

Author

Seiichi Manyama, May 12 2024

Status

approved