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A160467 The fifth factor of the row sums of the Eta triangle A160464 3
1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 16, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 32, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Fifth factor of the row sums A160466 of the Eta triangle A160464.

Contribution from Peter Luschny, May 31 2009: (Start)

Let odd(n) by the characteristic function of the odd numbers (A000035) and sigma(n) the number of 1's in binary expansion of n (A000120) then

a(n) = 2^(sigma(n-1)-sigma(n)+odd(n)).

Let B_{n} be the Bernoulli number. Then this sequence is also

a(n) = denominator(4*(4^n-1)*B_{2*n}/n). (End)

LINKS

Table of n, a(n) for n=1..96.

FORMULA

a(n) = A026741(n)/(A000265(n). - Paul Curtz, Apr 18 2010

a(n) = 2^max(A007814(n)-1,0). - Max Alekseyev, Feb 09 2011

a((2*n-1)*2^p) = A011782(p) , p >= 0 and n >= 1. - Johannes W. Meijer, Jan 25 2013

MAPLE

nmax:=96: p:= floor(log[2](nmax)): for n from 1 to nmax do a(n):=1 end do: for q from 1 to p do for n from 1 to nmax do if n mod 2^q = 0 then a(n):= 2^(q-1) end if: end do: end do: seq(a(n), n=1..nmax);

Contribution from Peter Luschny, May 31 2009: (Start)

a := proc(n) local sigma; sigma := proc(n) local i; add(i, i=convert(n, base, 2)) end; 2^(sigma(n-1)-sigma(n)+`if`(type(n, odd), 1, 0)) end: seq(a(n), n=1..96);

a := proc(n) denom(4*(4^n-1)*bernoulli(2*n)/n) end: seq(a(n), n=1..96); (End)

CROSSREFS

Cf. A220466.

Sequence in context: A054772 A085384 A067856 * A122374 A261960 A010121

Adjacent sequences:  A160464 A160465 A160466 * A160468 A160469 A160470

KEYWORD

base,easy,nonn,mult

AUTHOR

Johannes W. Meijer, May 24 2009, Jun 28 2011

EXTENSIONS

mult keyword added by Max Alekseyev, Feb 09 2011

STATUS

approved

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Last modified September 23 21:28 EDT 2017. Contains 292391 sequences.