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A141121
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G.f. A(x) satisfies A(A(A(A(A(A(x)))))) = x + 36*x^2.
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4
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1, 6, -180, 8640, -498960, 31434480, -2055943296, 135216506304, -8720972739072, 538646016002688, -31024094144060160, 1609593032459782656, -71392972690228672512, 2461961564459510280192, -51302015299696881770496, -415041229811424576835584
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OFFSET
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1,2
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LINKS
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FORMULA
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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) = 1/6 * ( 36^(n-m) * binomial(m,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) + Sum_{h=i..n} b(n,h) * b(h,i)) * b(i,j)) * b(j,k)) * b(k,l)) * b(l,m) ). a(n) = b(n,1).
A(A(x)) = F(4*x)/4, where F(x) is the g.f. for A141118.
A(A(A(x))) = G(9*x)/9, where G(x) is the g.f. for A027436. (End)
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EXAMPLE
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G.f.: A(x) = x + 6*x^2 - 180*x^3 + 8640*x^4 - 498960*x^5 +...
A(A(x)) = x + 12*x^2 - 288*x^3 + 12096*x^4 - 622080*x^5 +...
A(A(A(x))) = x + 18*x^2 - 324*x^3 + 11664*x^4 - 524880*x^5 +...
A(A(A(A(x)))) = x + 24*x^2 - 288*x^3 + 8640*x^4 - 331776*x^5 +...
A(A(A(A(A(x))))) = x + 30*x^2 - 180*x^3 + 4320*x^4 - 136080*x^5 +...
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PROG
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(PARI) {a(n, m=6)=local(F=x+m*x^2+x*O(x^n), G); if(n<1, 0, for(k=3, n, G=F+x*O(x^k); for(i=1, m-1, G=subst(F, x, G)); F=F+((-polcoeff(G, k))/m)*x^k); return(polcoeff(F, n, x)))}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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