0,2

Also denominators of partial sums sum(C(k)/(-4)^k,k=0..n)= A120788(n)/A120777(n).

One half of denominators of partial sums which involve Catalan numbers A000108(k) divided by 4^k with alternating signs.

The listed numbers coincide with the denominators of sum(C(k)/4^k,k=0..n). See numerators A120778. In general these denominators may be different. See e.g. A120783 versus A120793 and A120787 versus A120796.

a(n)=denominator(r(n)), with the rationals r(n) defined under A120088.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)

a(n) = denom(binomial(2*n+2,n+1)/2^(2*n+1))

If b(n) = log(a(n))/log(2) then c(n) = b(n+1)-b(n) = A001511(n+1) i.e. the ruler function.

(End)

Conjecture: The following Maple program appears to generate this sequence! Z[0]:=0: for k to 30 do Z[k]:=simplify(1/(2-z*Z[k-1])) od: g:=sum((Z[j]-Z[j-1]), j=1..30): gser:=series(g, z=0, 27): seq(denom(coeff(gser, z, n))/2, n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 21 2008

restart; nmax:=23; A001511 (1):=1: for n from 2 to nmax do A001511(n):= A001511(n-1)+(-1)^n* A001511(floor(n/2)) od: b(0):=0: for n from 1 to nmax do b(n):=b(n-1)+ A001511(n+1) od: for n from 0 to nmax-1 do a(n):=2^b(n) od: seq(a(n), n=0..nmax-1); [From Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)

Appears in A162446.

(End)

Sequence in context: A123106 A123288 A063083 this_sequence A091095 A075787 A086891

Adjacent sequences: A120774 A120775 A120776 this_sequence A120778 A120779 A120780

nonn,easy,frac

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006