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A170919 Write tan x = Prod_{n>=1} (1 + g_n x^n); a(n) = denominator(g_n). 2
1, 1, 3, 3, 5, 45, 105, 315, 2835, 14175, 5775, 467775, 6081075, 2837835, 212837625, 70945875, 3618239625, 97692469875, 206239658625, 9280784638125, 1031198293125, 142924083427125, 322279795963125, 101111706320625, 136968913284328125, 161872352063296875 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..26.

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, -1, 7/3, -14/3, 54/5, -1112/45, 6574/105, -48488/315, 1143731/2835, ...

MAPLE

L := 28: g := NULL:

t := series(tan(x), x, L):

for n from 1 to L-2 do

   c := coeff(t, x, n);

   t := series(t/(1 + c*x^n), x, L);

   g := g, c;

od: map(denom, [g]); # Based on Maple in A170918. Peter Luschny, Oct 05 2019

CROSSREFS

Cf. A170918, A170910-A170917.

Sequence in context: A200562 A093310 A256402 * A280779 A241591 A248592

Adjacent sequences:  A170916 A170917 A170918 * A170920 A170921 A170922

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 30 2010

STATUS

approved

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)