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A196839 Triangle of denominators of the coefficient of x^m in the n-th Bernoulli polynomial, 0 <= m <= n.

%I A196839 #34 Apr 10 2021 11:31:15
%S A196839 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 A196839 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 A196839 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 A196839 Triangle of denominators of the coefficient of x^m in the n-th Bernoulli polynomial, 0 <= m <= n.
%C A196839 The numerator triangle is found under A196838.
%C A196839 This is the row reversed triangle A053383.
%H A196839 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 A196839 T(n,m) = denominator([x^m]Bernoulli(n,x)), n>=0, m=0..n.
%F A196839 E.g.f. of Bernoulli(n,x): z*exp(x*z)/(exp(z)-1).
%F A196839 See the Graham et al. reference given in A196838, eq. (7.80), p. 354.
%F A196839 T(n,m) = denominator(binomial(n,m)*Bernoulli(n-m)). - _Fabián Pereyra_, Mar 04 2020
%e A196839 The triangle starts with
%e A196839 n\m 0  1  2  3  4  5  6  7  8 ...
%e A196839 0:  1
%e A196839 1:  2  1
%e A196839 2:  6  1  1
%e A196839 3:  1  2  2  1
%e A196839 4: 30  1  1  1  1
%e A196839 5:  1  6  1  3  2  1
%e A196839 6: 42  1  2  1  2  1  1
%e A196839 7:  1  6  1  6  1  2  2  1
%e A196839 8: 30  1  3  1  3  1  3  1  1
%e A196839 ...
%e A196839 For the start of the rational triangle A196838(n,m)/a(n,m) see the example section in A196838.
%p A196839 with(ListTools):with(PolynomialTools):
%p A196839 CoeffList := p -> CoefficientList(p, x):
%p A196839 Trow := n -> denom(CoeffList(bernoulli(n, x))):
%p A196839 Flatten([seq(Trow(n), n = 0..12)]); # _Peter Luschny_, Apr 10 2021
%Y A196839 Three versions of coefficients of Bernoulli polynomials: A053382/A053383; for reflected version see A196838/A196839; see also A048998 and A048999.
%K A196839 nonn,easy,tabl,frac
%O A196839 0,2
%A A196839 _Wolfdieter Lang_, Oct 23 2011
%E A196839 Name edited by _M. F. Hasler_, Mar 09 2020