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A068369
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Numerators of coefficients of a formal power series solution of f''(x) = f(f(x)).
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0
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1, 1, 2, 14, 210, 5572, 245224, 16484608, 1592692724, 211735948032, 37486076895064, 8611994418091904, 2512364155208956104, 913526595412940173952, 407407936880027138109376
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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.
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LINKS
| sci.math thread, f''(x)=f(f(x))
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EXAMPLE
| f(x) = x + 1/6*x^3 + 2/120*x^5 + 14/5040*x^7 + ...
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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]
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CROSSREFS
| Sequence in context: A122647 A158097 A136550 * A034405 A197210 A153668
Adjacent sequences: A068366 A068367 A068368 * A068370 A068371 A068372
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org), Mar 01 2002
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 06 2002
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