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A372521
G.f. A(x) satisfies A(A(A(A(A(x))))) = x + 5*x^2 + 25*x^3.
2
0, 1, 1, 1, -24, 176, -524, -5124, 87126, -506774, -1759824, 57671226, -358791624, -2206347624, 49453238976, -92944954824, -4824317301399, 31062072140001, 557647434392001, -6058153265478399, -93734220877891074, 1402372000511972226, 21436083233577492876
OFFSET
0,5
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) * Sum_{l=0..m} binomial(l,n-3*m+2*l) * binomial(m,l) - 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 04 2024
STATUS
approved