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

Author

Wouter Meeussen, Dec 07 2003

Keywords

• nonn

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

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)

Programs

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}]

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