|
| |
|
|
A123851
|
|
A cubic recurrence: a(0) = 1, a(n) = n*a(n-1)^3.
|
|
8
| |
|
|
1, 1, 2, 24, 55296, 845378412871680, 3624972460853492659595005581182702601633792000, 3334357599191948698197009417320642209065051866861904861213566953849866162801
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| A cubic analog of Somos's quadratic recurrence sequence A052129.
|
|
|
REFERENCES
| Sung-Hyuk Cha, On the k-ary Tree Combinatorics, http://csis.pace.edu/~scha/CompComb/CSISTR11-284.pdf
S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl. 332 (2007) 292-314.
|
|
|
LINKS
| J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant
Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant
|
|
|
FORMULA
| a(n) ~ c^(3^n)*n^(-1/2)/(1 + 3/4n - 15/32n^2 + 113/128n^3 + ...) where c = 1.1563626843322... is the cubic recurrence constant A123852.
|
|
|
EXAMPLE
| a(3) = 3*a(2)^3 = 3*(2*a(1)^3)^3 = 3*(2*(1*a(0)^3)^3)^3 = 3*(2*(1*1^3)^3)^3 = 3*(2*1)^3 = 3*8 = 24.
|
|
|
MATHEMATICA
| (a[n_] := If[n==0, 1, n*a[n-1]^3]; Table[a[n], {n, 0, 7}])
|
|
|
CROSSREFS
| Cf. A052129, A112302, A116603, A123852, A123853, A123854.
Sequence in context: A108349 A000722 A098679 * A120122 A068943 A100815
Adjacent sequences: A123848 A123849 A123850 * A123852 A123853 A123854
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Petros Hadjicostas and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 15 2006
|
| |
|
|
