A170924 - OEIS

%I #19 Jul 23 2023 17:00:59

%S 1,3,1,27,3,39,9,2955,7,1737,93,88047,315,79779,1083,77010795,3855,

%T 488391,13797,905252529,49689,204066351,182361,756251509503,10485,

%U 10978530465,619549,10462007147787,9256395,603860858253,34636833,150202954242966315

%N a(n) = numerator of the coefficient c(n) of x^n in (1/sqrt(1-x))/Product_{k=1..n-1} 1 + c(k)*x^k, n = 1, 2, 3, ...

%H 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 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 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 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 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 Wolfdieter Lang, <a href="/A157162/a157162.txt">Recurrences for the general problem</a>.

%e 1/2, 3/8, 1/8, 27/128, 3/32, 39/512, 9/128, 2955/32768, 7/128, ...

%p L := 34: g := NULL:

%p t := series(1/sqrt(1 - x), x, L):

%p for n from 1 to L-2 do

%p    c := coeff(t, x, n);

%p    t := series(t/(1 + c*x^(n)), x, L);

%p    g := g, c;

%p od: map(numer, [g]); # _Peter Luschny_, May 12 2022

%Y Cf. A170923 (denominators).

%Y Cf. A353583 / A353584 for power product expansion of 1 + tan x.

%Y Cf. A353586 / A353587 for power product expansion of (tan x)/x.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, Jan 31 2010

%E Following a suggestion from _Ilya Gutkovskiy_, name corrected so that it matches the data by _Peter Luschny_, May 12 2022