A089170 Numerator of 2*BernoulliB[2*(n+1)]*(4^(n+1)-1)/(2*(n+1))] divided by numerator of the series coefficients of 1/(1 + Cosh[x]).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 527, 1, 1, 1, 1, 31, 1, 1, 731, 1, 41, 1, 1, 1, 37, 1333, 17, 1, 1, 1, 31, 1, 1, 1, 17, 73, 1, 1, 1, 43, 1271, 59, 629, 1, 73, 2759, 43, 1, 1, 1, 17, 1, 67, 7519, 1, 31, 89, 1, 289, 1, 29020032511, 1, 10573, 1, 1, 1, 2227, 486029

Offset

0,12

Comments

Ratios of two similar sequences.

This sequence is related to the sequences of the numerators and denominators of the Taylor series for tan(x), i.e., A002430 and A036279, and the similar sequences A160469 and A156769. - Johannes W. Meijer, May 24 2009

Links

Michael De Vlieger, Table of n, a(n) for n = 0..5000

Formula

For n>=0, a(n)=c(n+1) where c(n)=numerator((4^n-1)*B(2*n)/n)/numerator((4^n-1)*B(2*n)/(2*n)!), B(k) denotes the k-th Bernoulli number. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Maple

seq(numer(2*bernoulli(2*n)*(4^n-1)/(2*n))/numer((4^n-1)*bernoulli(2*n)/(2*n)!), n=1..100); # C. Ronaldo

Mathematica

Table[Numerator[2*BernoulliB[2*n]*(4^n -1)/(2*n)]/Numerator[SeriesCoefficient[Series[1/(1+Cosh[x]), {x, 0, 2n}], 2n-2]], {n, 1, 128}]

Crossrefs

Cf. A002425.

From Johannes W. Meijer, May 24 2009: (Start)

Equals A160469(n+1)/A002430(n+1).

Equals A156769(n+1)/A036279(n+1).

(End)

Sequence in context: A176728 A300909 A088469 * A040292 A040293 A351307

Adjacent sequences: A089167 A089168 A089169 * A089171 A089172 A089173

Keyword

nonn

Author

Wouter Meeussen, Dec 07 2003

Status

approved