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A170923
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a(n) = denominator of the coefficient c(n) of x^n in sqrt(1+x)/Product_{0 < k < n} 1 + c(k)*x^k, n = 1, 2, 3, ...
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2
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2, 8, 8, 128, 32, 512, 128, 32768, 128, 32768, 2048, 2097152, 8192, 2097152, 32768, 2147483648, 131072, 16777216, 524288, 34359738368, 2097152, 8589934592, 8388608, 35184372088832, 524288, 549755813888, 33554432, 562949953421312, 536870912, 35184372088832
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..30.
Giedrius Alkauskas, One curious proof of Fermat's little theorem, arXiv:0801.0805 [math.NT], 2008.
Giedrius Alkauskas, A curious proof of Fermat's little theorem, Amer. Math. Monthly 116(4) (2009), 362-364.
Giedrius Alkauskas, Algebraic functions with Fermat property, eigenvalues of transfer operator and Riemann zeros, and other open problems, arXiv:1609.09842 [math.NT], 2016.
H. Gingold, H. W. Gould, and Michael E. Mays, Power Product Expansions, Utilitas Mathematica 34 (1988), 143-161.
H. Gingold and A. Knopfmacher, Analytic properties of power product expansions, Canad. J. Math. 47 (1995), 1219-1239.
Wolfdieter Lang, Recurrences for the general problem.
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MAPLE
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L := 32: g := NULL:
t := series(sqrt(1+x), x, L):
for n from 1 to L-2 do
c := coeff(t, x, n);
t := series(t/(1 + c*x^n), x, L);
g := g, c;
od: map(denom, [g]); # Peter Luschny, May 12 2022
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CROSSREFS
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Cf. A170922 (numerators).
Cf. A353583 / A353584 for power product expansion of 1 + tan x.
Cf. A353586 / A353587 for power product expansion of (tan x)/x.
Sequence in context: A181130 A212196 A156052 * A083523 A202619 A202379
Adjacent sequences: A170920 A170921 A170922 * A170924 A170925 A170926
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane, Jan 31 2010
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EXTENSIONS
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Following a suggestion from Ilya Gutkovskiy, name corrected so that it matches the data. - Peter Luschny, May 12 2022
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STATUS
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approved
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