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A170924
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, ...
0
1, 3, 1, 27, 3, 39, 9, 2955, 7, 1737, 93, 88047, 315, 79779, 1083, 77010795, 3855, 488391, 13797, 905252529, 49689, 204066351, 182361, 756251509503, 10485, 10978530465, 619549, 10462007147787, 9256395, 603860858253, 34636833, 150202954242966315
OFFSET
1,2
LINKS
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.
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.
EXAMPLE
1/2, 3/8, 1/8, 27/128, 3/32, 39/512, 9/128, 2955/32768, 7/128, ...
MAPLE
L := 34: g := NULL:
t := series(1/sqrt(1 - 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(numer, [g]); # Peter Luschny, May 12 2022
CROSSREFS
Cf. A170923 (denominators).
Cf. A353583 / A353584 for power product expansion of 1 + tan x.
Cf. A353586 / A353587 for power product expansion of (tan x)/x.
Sequence in context: A300457 A289329 A033464 * A173007 A113099 A317930
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jan 31 2010
EXTENSIONS
Following a suggestion from Ilya Gutkovskiy, name corrected so that it matches the data by Peter Luschny, May 12 2022
STATUS
approved