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A290638
Denominators of the sequence 1, 1/2, (1/2)/(3/4), ((1/2)/(3/4))/((5/6)/(7/8)), ... .
2
1, 2, 3, 10, 405, 204102, 391202754597, 6970736012254534531250, 3928936098952203755159851968781175221199855588403024634921875
OFFSET
0,2
COMMENTS
See A290637.
REFERENCES
See A290637.
LINKS
EXAMPLE
f(3): 1*4*6*7/(2*3*5*8) = 7/10, hence a(3)=10.
MAPLE
g:= (i, j)-> `if`(j=0, i, g(i, j-1)/g(i+2^(j-1), j-1)):
a:= n-> denom(g(1, n)):
seq(a(n), n=0..10); # Alois P. Heinz, Aug 08 2017
MATHEMATICA
f[1] = id[1]/id[2]; f[n_] := f[n] = f[n-1]/(f[n-1] /. id[k_] :> id[k+2^(n-1)]); a[n_]:= f[n] /. id -> Identity//Denominator; Array[a, 8]
PROG
(Python)
from sympy.core.cache import cacheit
from sympy import denom, Rational
@cacheit
def g(i, j): return Rational(i) if j==0 else g(i, j - 1)/g(i + 2**(j - 1), j - 1)
def a(n): return denom(g(1, n))
print([a(n) for n in range(12)]) # Indranil Ghosh, Aug 09 2017, after Maple code
CROSSREFS
Cf. A290637 (numerators), A094542 (supersequence).
Sequence in context: A132536 A322067 A302250 * A330294 A270442 A330581
KEYWORD
nonn,frac
AUTHOR
STATUS
approved