cp's OEIS Frontend

A170918 a(n) = numerator of the coefficient c(n) of x^n in (tan x)/Product_{0 < k < n} 1 + c(k)*x^k, n = 1, 2, 3, ...

%I A170918 #26 Jul 23 2023 15:45:13
%S A170918 1,-1,7,-14,54,-1112,6574,-48488,1143731,-14813072,16252211,
%T A170918 -3500388967,125127865048,-158589803803,33133618166566,
%U A170918 -30512906279732,4378989933312913,-330336346477870319,1981395373839282068,-251479418962683770473,79893293800974935213,-31493610597939643431532
%N A170918 a(n) = numerator of the coefficient c(n) of x^n in (tan x)/Product_{0 < k < n} 1 + c(k)*x^k, n = 1, 2, 3, ...
%H A170918 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 A170918 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 A170918 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 A170918 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 A170918 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 A170918 Wolfdieter Lang, <a href="/A157162/a157162.txt">Recurrences for the general problem</a>.
%e A170918 1, -1, 7/3, -14/3, 54/5, -1112/45, 6574/105, -48488/315, 1143731/2835, ...
%p A170918 t1:=tan(x);
%p A170918 L:=100;
%p A170918 t0:=series(t1,x,L):
%p A170918 g:=[]; M:=40; t2:=t0:
%p A170918 for n from 1 to M do
%p A170918 t3:=coeff(t2,x,n); t2:=series(t2/(1+t3*x^n),x,L); g:=[op(g),t3];
%p A170918 od:
%p A170918 g;
%p A170918 g1:=map(numer,g);
%p A170918 g2:=map(denom,g);
%o A170918 (PARI) t=tan(x+O(x)^25); vector(#t,n,c=polcoef(t,n);t/=1+c*x^n;numerator(c)) \\ _M. F. Hasler_, May 07 2022
%Y A170918 Cf. A170919 (denominators), A170910-A170917.
%Y A170918 Cf. A353583 / A353584 for power product expansion of 1 + tan x.
%Y A170918 Cf. A353586 / A353587 for power product expansion of (tan x)/x.
%K A170918 sign,frac
%O A170918 1,3
%A A170918 _N. J. A. Sloane_, Jan 30 2010
%E A170918 Following a suggestion from _Ilya Gutkovskiy_, name corrected so that it matches the data by _M. F. Hasler_, May 07 2022