A372736 E.g.f. A(x) satisfies A(A(A(A(x)))) = x * exp(4*x).

0, 1, 2, -6, 64, -1000, 18456, -323456, 2260672, 234740736, -17575841600, 599924638016, 9410095550208, -2115023122095104, -46248172033366016, 29749517096905651200, -1275218259853989392384, -512185830428775541448704, 72072305653906206009335808

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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) = 1/4 * ( (4*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) * b(j,k)) * b(k,l)) * b(l,m) ). a(n) = b(n,1).

Crossrefs

Cf. A199852, A372737, A372745.

Sequence in context: A347949 A241590 A052522 * A193609 A061999 A066756

Adjacent sequences: A372733 A372734 A372735 * A372737 A372738 A372739

Keyword

sign

Author

Seiichi Manyama, May 11 2024

Status

approved