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A170923 a(n) = denominator of the coefficient c(n) of x^n in sqrt(1+x)/Product_{k=1..n-1} 1 + c(k)*x^k, n = 1, 2, 3, ...

%I A170923 #19 Jul 23 2023 18:23:52
%S A170923 2,8,8,128,32,512,128,32768,128,32768,2048,2097152,8192,2097152,32768,
%T A170923 2147483648,131072,16777216,524288,34359738368,2097152,8589934592,
%U A170923 8388608,35184372088832,524288,549755813888,33554432,562949953421312,536870912,35184372088832
%N A170923 a(n) = denominator of the coefficient c(n) of x^n in sqrt(1+x)/Product_{k=1..n-1} 1 + c(k)*x^k, n = 1, 2, 3, ...
%H A170923 Giedrius Alkauskas, <a href="http://arxiv.org/abs/0801.0805">One curious proof of Fermat's little theorem</a>, arXiv:0801.0805 [math.NT], 2008.
%H A170923 Giedrius Alkauskas, <a href="https://www.jstor.org/stable/40391097">A curious proof of Fermat's little theorem</a>, Amer. Math. Monthly 116(4) (2009), 362-364.
%H A170923 Giedrius Alkauskas, <a href="https://arxiv.org/abs/1609.09842">Algebraic functions with Fermat property, eigenvalues of transfer operator and Riemann zeros, and other open problems</a>, arXiv:1609.09842 [math.NT], 2016.
%H A170923 H. Gingold, H. W. Gould, and Michael E. Mays, <a href="https://www.researchgate.net/publication/268023169_Power_product_expansions">Power Product Expansions</a>, Utilitas Mathematica 34 (1988), 143-161.
%H A170923 H. Gingold and A. Knopfmacher, <a href="http://dx.doi.org/10.4153/CJM-1995-062-9">Analytic properties of power product expansions</a>, Canad. J. Math. 47 (1995), 1219-1239.
%H A170923 Wolfdieter Lang, <a href="/A157162/a157162.txt">Recurrences for the general problem</a>.
%p A170923 L := 32: g := NULL:
%p A170923 t := series(sqrt(1+x), x, L):
%p A170923 for n from 1 to L-2 do
%p A170923    c := coeff(t, x, n);
%p A170923    t := series(t/(1 + c*x^n), x, L);
%p A170923    g := g, c;
%p A170923 od: map(denom, [g]); # _Peter Luschny_, May 12 2022
%Y A170923 Cf. A170922 (numerators).
%Y A170923 Cf. A353583 / A353584 for power product expansion of 1 + tan x.
%Y A170923 Cf. A353586 / A353587 for power product expansion of (tan x)/x.
%K A170923 nonn,frac
%O A170923 1,1
%A A170923 _N. J. A. Sloane_, Jan 31 2010
%E A170923 Following a suggestion from _Ilya Gutkovskiy_, name corrected so that it matches the data by _Peter Luschny_, May 12 2022