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

6, 120, 840, 362880, 14968800, 9340531200, 49037788800, 3201186852864000, 8485288812000, 182467650613248000, 908859963476424960000, 1424498881530396672000000, 10633661572674172032000000, 8289151869130970582384640000000, 1720739115690134518218240000000, 97858575719142221963014963200000000

Offset

1,1

Links

Table of n, a(n) for n=1..16.

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.

W. Lang, Recurrences for the general problem.

Example

-1/6, 1/120, 1/840, 73/362880, 353/14968800, 36499/9340531200, 24257/49037788800, ...

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

Crossrefs

Cf. A170916, A170912-A170915.

Sequence in context: A076234 A066289 A351862 * A115678 A048604 A001516

Adjacent sequences: A170914 A170915 A170916 * A170918 A170919 A170920

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 30 2010

Status

approved