%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