login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A196839 Triangle of denominators of the coefficient of x^m in the n-th Bernoulli polynomial, 0 <= m <= n. 24

%I #34 Apr 10 2021 11:31:15

%S 1,2,1,6,1,1,1,2,2,1,30,1,1,1,1,1,6,1,3,2,1,42,1,2,1,2,1,1,1,6,1,6,1,

%T 2,2,1,30,1,3,1,3,1,3,1,1,1,10,1,1,1,5,1,1,2,1,66,1,2,1,1,1,1,1,2,1,1,

%U 1,6,1,2,1,1,1,1,1,6,2,1,2730,1,1,1,2,1,1,1,2,1,1,1,1

%N Triangle of denominators of the coefficient of x^m in the n-th Bernoulli polynomial, 0 <= m <= n.

%C The numerator triangle is found under A196838.

%C This is the row reversed triangle A053383.

%H D. H. Lehmer, <a href="http://www.jstor.org/stable/2322383">A new approach to Bernoulli polynomials</a>, The American mathematical monthly 95.10 (1988): 905-911.

%F T(n,m) = denominator([x^m]Bernoulli(n,x)), n>=0, m=0..n.

%F E.g.f. of Bernoulli(n,x): z*exp(x*z)/(exp(z)-1).

%F See the Graham et al. reference given in A196838, eq. (7.80), p. 354.

%F T(n,m) = denominator(binomial(n,m)*Bernoulli(n-m)). - _Fabián Pereyra_, Mar 04 2020

%e The triangle starts with

%e n\m 0 1 2 3 4 5 6 7 8 ...

%e 0: 1

%e 1: 2 1

%e 2: 6 1 1

%e 3: 1 2 2 1

%e 4: 30 1 1 1 1

%e 5: 1 6 1 3 2 1

%e 6: 42 1 2 1 2 1 1

%e 7: 1 6 1 6 1 2 2 1

%e 8: 30 1 3 1 3 1 3 1 1

%e ...

%e For the start of the rational triangle A196838(n,m)/a(n,m) see the example section in A196838.

%p with(ListTools):with(PolynomialTools):

%p CoeffList := p -> CoefficientList(p, x):

%p Trow := n -> denom(CoeffList(bernoulli(n, x))):

%p Flatten([seq(Trow(n), n = 0..12)]); # _Peter Luschny_, Apr 10 2021

%Y Three versions of coefficients of Bernoulli polynomials: A053382/A053383; for reflected version see A196838/A196839; see also A048998 and A048999.

%K nonn,easy,tabl,frac

%O 0,2

%A _Wolfdieter Lang_, Oct 23 2011

%E Name edited by _M. F. Hasler_, Mar 09 2020

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)