The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A185425 Bisection of A185424. Numerators of even-indexed generalized Bernoulli numbers associated with the zigzag numbers A000111. 2
 1, 1, 19, 253, 3319, 222557, 422152729, 59833795, 439264083023, 76632373664299, 4432283799315809, 317829581058418253, 1297298660169509319229, 696911453333335463719, 28877308885785768720478751, 157040990105362922778773747849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let E(t) = sec(t)+tan(t) denote the generating function for the zigzag numbers A000111. The zigzag Bernoulli numbers, denoted ZB(n), are defined by means of the generating function log E(t)/(E(t)-1) = Sum_{n>=0} ZB(n)*t^n/n!. See formula (1). The present sequence lists the numerators of ZB(2*n) for n>=0. LINKS G. C. Greubel, Table of n, a(n) for n = 0..235 FORMULA (1)... 1/2*log(sec(t)+tan(t))*(1+sin(t)+cos(t))/(1+sin(t)-cos(t)) = Sum_{n >= 0} ZB(2*n)*t^(2*n)/(2*n)! = 1 + (1/6)*t^2/2! + (19/30)*t^4/4! + (253/42)*t^6/6! + .... (2)... ZB(2*n) = (-1)^n*Sum_{k = 0..n} binomial(2*n,2*k)/(2*k+1)* Bernoulli(2*n-2*k)*Euler(2*k). (3)... a(n) = numerator(ZB(2*n)). MAPLE a := n - > (-1)^n*add (binomial(2*n, 2*k)/(2*k+1)* bernoulli(2*n-2*k)* euler(2*k), k = 0..n): seq(numer(a(n)), n = 0..20); MATHEMATICA Numerator[Table[(-1)^n*Sum[Binomial[2*n, 2*k]*BernoulliB[2*(n - k)]* EulerE[2*k]/(2*k + 1), {k, 0, n}], {n, 0, 50}]] (* G. C. Greubel, Jul 06 2017 *) CROSSREFS Cf. A000111, A027641, A000367, A185424. Sequence of denominators is A002445. Sequence in context: A009762 A017952 A055433 * A009728 A027532 A021394 Adjacent sequences:  A185422 A185423 A185424 * A185426 A185427 A185428 KEYWORD nonn,easy AUTHOR Peter Bala, Feb 18 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 17 12:01 EDT 2021. Contains 343971 sequences. (Running on oeis4.)