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A123854
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Denominators in asymptotic expansion of cubic recurrence sequence A123851.
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7
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1, 4, 32, 128, 2048, 8192, 65536, 262144, 8388608, 33554432, 268435456, 1073741824, 17179869184, 68719476736, 549755813888, 2199023255552, 140737488355328, 562949953421312, 4503599627370496, 18014398509481984
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A cubic analog of the asymptotic expansion A116603 of Somos's quadratic recurrence sequence A052129. Numerators are A123853.
Equals 2^A004134(n); also the denominators in expansion of (1-x)^{-1/4}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2006
All terms are powers of 2. Log[2,a(n)] = A004134(n) = 3n - A000120(n) = {0, 2, 5, 7, 11, 13, 16, 18, 23, 25, 28, 30, 34, 36, 39, 41, 47, 49, 52, 54, 58, 60, 63, 65, 70, 72, 75, 77, 81, 83, 86, 88, 95, 97, 100, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2006
Is this the same sequence as A088802? - N. J. A. Sloane (njas(AT)research.att.com), Mar 21, 2007
Almost certainly this is the same as A088802. - Michael Somos Aug 23 2007
Denominators of Gegenbauer_C(2n,1/4,2). The denominators of Gegenbauer_C(n,1/4,2) give the doubled sequence. [From Paul Barry (pbarry(AT)wit.ie), Apr 21 2009]
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REFERENCES
| 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.
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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
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FORMULA
| a(n) = 2^A004134[n]. a(n) = 2^(3n - A000120(n)). - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2006
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EXAMPLE
| A123851(n) ~ c^(3^n)*n^(- 1/2)/(1 + 3/4n - 15/32n^2 + 113/128n^3 - 5397/2048n^4 + ...) where c = 1.1563626843322... is the cubic recurrence constant A123852.
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MAPLE
| f:=proc(t, x) exp(sum(ln(1+m*x)/t^m, m=1..infinity)); end; for j from 0 to 29 do denom(coeff(series(f(3, x), x=0, 30), x, j)); od;
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CROSSREFS
| Cf. A052129, A112302, A116603, A123851, A123852, A123853.
Cf. A004134, A004130, A000120.
Sequence in context: A033430 A088658 A088802 * A113154 A083299 A018215
Adjacent sequences: A123851 A123852 A123853 * A123855 A123856 A123857
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KEYWORD
| frac,nonn
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AUTHOR
| Petros Hadjicostas and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 15 2006
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