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A372499
G.f. satisfies A(A(A(x))) = F(x), where F(x) is the g.f. for A053540(n) = n*9^(n-1).
4
0, 1, 6, 9, 54, 0, -1944, 44469, -323676, -5990193, 179194032, 484654509, -105337511100, 757846026261, 85419734244300, -1707846638480514, -90276038133498612, 3464956887464464164, 118426852966952180502, -7984363576091338944720, -181143285020960488524558
OFFSET
0,3
LINKS
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) = 1/3 * ( 9^(n-m) * binomial(n+m-1,2*m-1) - Sum_{l=m+1..n-1} (b(n,l) + Sum_{k=l..n} b(n,k) * b(k,l)) * b(l,m) ). a(n) = b(n,1).
EXAMPLE
A(A(x)) = x + 12*x^2 + 90*x^3 + 594*x^4 + 3807*x^5 + 20412*x^6 + 123201*x^7 + 1032264*x^8 - 1463103*x^9 - 35468766*x^10 + ...
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 03 2024
STATUS
approved