A141121 G.f. A(x) satisfies A(A(A(A(A(A(x)))))) = x + 36*x^2.

1, 6, -180, 8640, -498960, 31434480, -2055943296, 135216506304, -8720972739072, 538646016002688, -31024094144060160, 1609593032459782656, -71392972690228672512, 2461961564459510280192, -51302015299696881770496, -415041229811424576835584

Offset: 1

Author

Paul D. Hanna, Jun 05 2008

Keywords

• sign

Examples

			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 +...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A027436, A141118, A141119, A141120.

Programs

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)))}

Formula

From Seiichi Manyama, May 04 2024: (Start)

Define the sequence b(n,m) as follows. If n

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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