A170916 Write sin(x)/x = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = numerator(g_n).
-1, 1, 1, 73, 353, 36499, 24257, 302426881, 87721, 348958703, 226786069421, 62199570679633, 62531659610839, 8559230855533306387, 235495453816743509, 2644298730170939345197, 281737789368631676609, 39043444996461526437828311, 6203284926188598376335167
Offset: 1
Examples
-1/6, 1/120, 1/840, 73/362880, 353/14968800, 36499/9340531200, 24257/49037788800, ...
Links
- 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.
- 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.
- W. Lang, Recurrences for the general problem.
Programs
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Maple
t1:=sin(x)/x; L:=100; t0:=series(t1, x, L): g:=[]; M:=40; t2:=t0: for n from 1 to M do t3:=coeff(t2, x, n); t2:=series(t2/(1+t3*x^n), x, L); g:=[op(g), t3]; od: g; h:=[seq(g[2*n], n=1..nops(g)/2)]; h1:=map(numer, h); h2:=map(denom, h); # Petros Hadjicostas, Oct 04 2019 by modifying N. J. A. Sloane's program from A170912 and A170913