cp's OEIS Frontend

A170919 a(n) = denominator of the coefficient c(n) of x^n in (tan x)/Product_{k=1..n-1} 1 + c(k)*x^k, n = 1, 2, 3, ...

%I A170919 #23 Jul 23 2023 16:45:25
%S A170919 1,1,3,3,5,45,105,315,2835,14175,5775,467775,6081075,2837835,
%T A170919 212837625,70945875,3618239625,97692469875,206239658625,9280784638125,
%U A170919 1031198293125,142924083427125,322279795963125,101111706320625,136968913284328125,161872352063296875
%N A170919 a(n) = denominator of the coefficient c(n) of x^n in (tan x)/Product_{k=1..n-1} 1 + c(k)*x^k, n = 1, 2, 3, ...
%H A170919 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 A170919 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 A170919 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 A170919 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 A170919 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 A170919 Wolfdieter Lang, <a href="/A157162/a157162.txt">Recurrences for the general problem</a>.
%e A170919 1, -1, 7/3, -14/3, 54/5, -1112/45, 6574/105, -48488/315, 1143731/2835, ...
%p A170919 L := 28: g := NULL:
%p A170919 t := series(tan(x), x, L):
%p A170919 for n from 1 to L-2 do
%p A170919    c := coeff(t, x, n);
%p A170919    t := series(t/(1 + c*x^n), x, L);
%p A170919    g := g, c;
%p A170919 od: map(denom, [g]); # Based on Maple in A170918. - _Peter Luschny_, Oct 05 2019
%Y A170919 Cf. A170918 (numerators), A170910-A170917.
%Y A170919 Cf. A353583 / A353584 for power product expansion of 1 + tan x.
%Y A170919 Cf. A353586 / A353587 for power product expansion of (tan x)/x.
%K A170919 nonn,frac
%O A170919 1,3
%A A170919 _N. J. A. Sloane_, Jan 30 2010
%E A170919 Following a suggestion from _Ilya Gutkovskiy_, name corrected so that it matches the data by _Peter Luschny_, May 12 2022