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Search: id:A123851
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| A123851 |
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Cubic recurrence sequence a(0) = 1, a(n) = n*a(n-1)^3. |
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+0
7
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| 1, 1, 2, 24, 55296, 845378412871680, 3624972460853492659595005581182702601633792000, 3334357599191948698197009417320642209065051866861904861213566953849866162801
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A cubic analog of Somos's quadratic recurrence sequence A052129.
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REFERENCES
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S. 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. (to appear).
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LINKS
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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
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FORMULA
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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.
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EXAMPLE
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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.
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MATHEMATICA
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(a[n_] := If[n==0, 1, n*a[n-1]^3]; Table[a[n], {n, 0, 7}])
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CROSSREFS
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Cf. A052129, A112302, A116603, A123852, A123853, A123854.
Adjacent sequences: A123848 A123849 A123850 this_sequence A123852 A123853 A123854
Sequence in context: A108349 A000722 A098679 this_sequence A120122 A068943 A100815
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KEYWORD
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easy,nonn
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AUTHOR
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Petros Hadjicostas and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 15 2006
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