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A068369 Numerators of coefficients of a formal power series solution of f''(x) = f(f(x)). 0
1, 1, 2, 14, 210, 5572, 245224, 16484608, 1592692724, 211735948032, 37486076895064, 8611994418091904, 2512364155208956104, 913526595412940173952, 407407936880027138109376 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Define f(x)=sum for n>=0 of a(n)/(2n+1)!*x^(2n+1). Formally this satisfies f''(x) = f(f(x)), but the series diverges.
LINKS
sci.math thread, 2/18/02 by William Elliot: f''(x)=f(f(x))
EXAMPLE
f(x) = x + 1/6*x^3 + 2/120*x^5 + 14/5040*x^7 + ...
MATHEMATICA
b[1]=1; b[n_] := Module[{f, bn}, If[EvenQ[n], Return[b[n]=0]]; f=Series[Sum[b[k]*x^k, {k, 1, n-2, 2}]+bn*x^n, {x, 0, n}]; b[n]=Solve[Coefficient[D[f, {x, 2}]-(f/.x->f), x, n-2]==0, bn][[1, 1, 2]]]; a[n_] := (2n+1)!b[2n+1]
CROSSREFS
Sequence in context: A262003 A271847 A136550 * A034405 A197210 A153668
KEYWORD
nonn
AUTHOR
Joe Keane (jgk(AT)jgk.org), Mar 01 2002
EXTENSIONS
Edited by Dean Hickerson, Aug 06 2002
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)