A367321 Numerators of the coefficients in the Taylor expansion of the Lyapunov exponent for the Random Fibonacci sequence.

1, 7, 58, 555, 5686, 61510, 692084, 8029491, 95474398, 1158542962, 14301359788, 59716352682, 2272903748636, 29160850916204, 377850135826408, 4939485500738195, 65088291655161454, 863887932803327098, 11541609784040120316, 170640229753234495001

Offset

1,2

Comments

Expanding the Lyapunov exponent (c(beta)) as a power series in beta yields

c(beta) = -Sum_{n>=1} a(n)*beta^(2n)/(2n).

References

M. Embree and L. N. Trefethen, "Growth and decay of Random Fibonacci Sequences". Royal Society, Vol. 455, Issue 1987: 2471-2485 (1999).

C. Sire and P. L. Krapivsky, "Random Fibonacci Sequences". Journal of Physics A: Mathematical and General, Vol. 34 Issue 42: 9065-9083 (2001).

Links

Table of n, a(n) for n=1..20.

Crossrefs

Sequence in context: A081343 A163048 A318233 * A192940 A126130 A323254

Adjacent sequences: A367318 A367319 A367320 * A367322 A367323 A367324

Keyword

nonn

Author

Richard Mason, Nov 14 2023

Status

approved