|
Search: id:A068369
|
|
|
| A068369 |
|
Numerators of coefficients of a formal power series solution of f''(x) = f(f(x)). |
|
+0
1
|
|
| 1, 1, 2, 14, 210, 5572, 245224, 16484608, 1592692724, 211735948032, 37486076895064, 8611994418091904, 2512364155208956104, 913526595412940173952, 407407936880027138109376
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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, 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: A122647 A158097 A136550 this_sequence A034405 A153668 A105749
Adjacent sequences: A068366 A068367 A068368 this_sequence A068370 A068371 A068372
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joe Keane (jgk(AT)jgk.org), Mar 01 2002
|
|
EXTENSIONS
|
Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 06 2002
|
|
|
Search completed in 0.002 seconds
|
