cp's OEIS Frontend

A170916 Write sin(x)/x = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = numerator(g_n).

%I A170916 #16 Oct 06 2019 02:38:24
%S A170916 -1,1,1,73,353,36499,24257,302426881,87721,348958703,226786069421,
%T A170916 62199570679633,62531659610839,8559230855533306387,235495453816743509,
%U A170916 2644298730170939345197,281737789368631676609,39043444996461526437828311,6203284926188598376335167
%N A170916 Write sin(x)/x = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = numerator(g_n).
%H A170916 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 A170916 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 A170916 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 A170916 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 A170916 W. Lang, <a href="/A157162/a157162.txt">Recurrences for the general problem</a>.
%e A170916 -1/6, 1/120, 1/840, 73/362880, 353/14968800, 36499/9340531200, 24257/49037788800, ...
%p A170916 t1:=sin(x)/x;
%p A170916 L:=100;
%p A170916 t0:=series(t1, x, L):
%p A170916 g:=[]; M:=40; t2:=t0:
%p A170916 for n from 1 to M do
%p A170916 t3:=coeff(t2, x, n); t2:=series(t2/(1+t3*x^n), x, L); g:=[op(g), t3];
%p A170916 od:
%p A170916 g;
%p A170916 h:=[seq(g[2*n], n=1..nops(g)/2)];
%p A170916 h1:=map(numer, h);
%p A170916 h2:=map(denom, h); # _Petros Hadjicostas_, Oct 04 2019 by modifying _N. J. A. Sloane_'s program from A170912 and A170913
%Y A170916 Cf. A170917, A170912, A170913, A170914, A170915.
%K A170916 sign,frac
%O A170916 1,4
%A A170916 _N. J. A. Sloane_, Jan 30 2010