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A372736
E.g.f. A(x) satisfies A(A(A(A(x)))) = x * exp(4*x).
2
0, 1, 2, -6, 64, -1000, 18456, -323456, 2260672, 234740736, -17575841600, 599924638016, 9410095550208, -2115023122095104, -46248172033366016, 29749517096905651200, -1275218259853989392384, -512185830428775541448704, 72072305653906206009335808
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) = 1/4 * ( (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
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 11 2024
STATUS
approved