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A052105 Denominators of coefficients in function a(x) such that a(a(x)) = exp(x) - 1. 4
1, 1, 4, 48, 1, 3840, 92160, 645120, 3440640, 30965760, 14863564800, 24222105600, 7847962214400, 40809403514880, 5713316492083200, 7617755322777600, 5484783832399872000, 5328075722902732800, 1220613711064989696000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.52.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..120

Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation A^{2^n}(x)=F(x), arXiv:1302.1986 [math.CO], 2013.

EXAMPLE

x + 1/4*x^2 + 1/48*x^3 + 1/3840*x^5 - 7/92160*x^6 + 1/645120*x^7 + ...

MATHEMATICA

a[x_, n_] := Sum[c[k] x^k, {k, 0, n}] ;

f[x_, n_] := Series[Exp[x] - 1, {x, 0, n}] // Normal;

b[x_, n_] := Series[a[a[x, n], n], {x, 0, n}] // Normal;

eq[n_] := Thread[CoefficientList[f[x, n] - b[x, n], x] == 0] // Rest;

c[0] = 0; so[3] = Solve[eq[3], {c[1], c[2], c[3]}] // First;

so[n_] := so[n] = Solve[eq[n] /. Flatten[Table[so[k], {k, 3, n - 1}]], c[n]] // First

Array[c, 19, 0] /. Flatten[Table[so[k], {k, 3, 19}]] // Denominator

(* Jean-Fran├žois Alcover, Jun 08 2011 *)

CROSSREFS

Cf. A052104, A052122, A052123.

Sequence in context: A210828 A141040 A182102 * A010293 A225987 A178429

Adjacent sequences:  A052102 A052103 A052104 * A052106 A052107 A052108

KEYWORD

nonn,easy,nice,frac

AUTHOR

N. J. A. Sloane, Jan 22 2000

STATUS

approved

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Last modified November 14 16:58 EST 2018. Contains 317210 sequences. (Running on oeis4.)