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A170917 Write sin(x)/x = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = denominator(g_n).

%I A170917 #9 Oct 05 2019 02:49:58
%S A170917 6,120,840,362880,14968800,9340531200,49037788800,3201186852864000,
%T A170917 8485288812000,182467650613248000,908859963476424960000,
%U A170917 1424498881530396672000000,10633661572674172032000000,8289151869130970582384640000000,1720739115690134518218240000000,97858575719142221963014963200000000
%N A170917 Write sin(x)/x = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = denominator(g_n).
%H A170917 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 A170917 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 A170917 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 A170917 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 A170917 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 A170917 W. Lang, <a href="/A157162/a157162.txt">Recurrences for the general problem</a>.
%e A170917 -1/6, 1/120, 1/840, 73/362880, 353/14968800, 36499/9340531200, 24257/49037788800, ...
%p A170917 t1:=sin(x)/x;
%p A170917 L:=100;
%p A170917 t0:=series(t1, x, L):
%p A170917 g:=[]; M:=40; t2:=t0:
%p A170917 for n from 1 to M do
%p A170917 t3:=coeff(t2, x, n); t2:=series(t2/(1+t3*x^n), x, L); g:=[op(g), t3];
%p A170917 od:
%p A170917 g;
%p A170917 h:=[seq(g[2*n], n=1..nops(g)/2)];
%p A170917 h1:=map(numer, h);
%p A170917 h2:=map(denom, h); # _Petros Hadjicostas_, Oct 04 2019 by modifying _N. J. A. Sloane_'s program from A170912 and A170913
%Y A170917 Cf. A170916, A170912-A170915.
%K A170917 nonn,frac
%O A170917 1,1
%A A170917 _N. J. A. Sloane_, Jan 30 2010