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A141120 G.f. A(x) satisfies: A(A(A(A(A(x))))) = x + 25*x^2. 4
1, 5, -100, 3250, -127500, 5456250, -241875000, 10733906250, -463469531250, 18897269531250, -699306093750000, 21927485449218750, -487263216796875000, 923644008789062500, 602420821142578125000, -38171197412384033203125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..128

EXAMPLE

G.f.: A(x) = x + 5*x^2 - 100*x^3 + 3250*x^4 - 127500*x^5 +5456250*x^6+...

A(A(x)) = x + 10*x^2 - 150*x^3 + 4125*x^4 - 140000*x^5 +5162500*x^6+...

A(A(A(x))) = x + 15*x^2 - 150*x^3 + 3375*x^4 - 96250*x^5 +2931250*x^6+...

A(A(A(A(x)))) = x + 20*x^2 - 100*x^3 + 1750*x^4 - 40000*x^5 +918750*x^6+..

MAPLE

X[1]:= unapply(x+c[2]*x^2, x):

for i from 2 to 6 do

  S:= series((X[i-1]@@5)(x)-x-25*x^2, x, 2^(i-1)+1);

  Sol:=solve({seq(coeff(S, x, k), k=2^(i-2)+1..2^(i-1))}, {seq(c[k], k=2^(i-2)+1

..2^(i-1))});

  X[i]:= unapply(subs(Sol, X[i-1](x))+add(c[j]*x^j, j=2^(i-1)+1..2^(i)), x);

od:

seq(coeff(X[i](x), x, i), i=1..2^5)); # Robert Israel, Jul 20 2020

PROG

(PARI) {a(n, m=5)=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)))}

CROSSREFS

Cf. A027436, A141118, A141119, A141121.

Sequence in context: A208348 A128784 A078534 * A123668 A336427 A197200

Adjacent sequences:  A141117 A141118 A141119 * A141121 A141122 A141123

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jun 05 2008

STATUS

approved

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)