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URL: https://oeis.org/A196839

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A196839
Triangle of denominators of the coefficient of x^m in the n-th Bernoulli polynomial, 0 <= m <= n.
24
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, 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, 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
OFFSET
0,2
COMMENTS
The numerator triangle is found under A196838.
This is the row reversed triangle A053383.
LINKS
D. H. Lehmer, A new approach to Bernoulli polynomials, The American mathematical monthly 95.10 (1988): 905-911.
FORMULA
T(n,m) = denominator([x^m]Bernoulli(n,x)), n>=0, m=0..n.
E.g.f. of Bernoulli(n,x): z*exp(x*z)/(exp(z)-1).
See the Graham et al. reference given in A196838, eq. (7.80), p. 354.
T(n,m) = denominator(binomial(n,m)*Bernoulli(n-m)). - Fabián Pereyra, Mar 04 2020
EXAMPLE
The triangle starts with
n\m 0 1 2 3 4 5 6 7 8 ...
0: 1
1: 2 1
2: 6 1 1
3: 1 2 2 1
4: 30 1 1 1 1
5: 1 6 1 3 2 1
6: 42 1 2 1 2 1 1
7: 1 6 1 6 1 2 2 1
8: 30 1 3 1 3 1 3 1 1
...
For the start of the rational triangle A196838(n,m)/a(n,m) see the example section in A196838.
MAPLE
with(ListTools):with(PolynomialTools):
CoeffList := p -> CoefficientList(p, x):
Trow := n -> denom(CoeffList(bernoulli(n, x))):
Flatten([seq(Trow(n), n = 0..12)]); # Peter Luschny, Apr 10 2021
CROSSREFS
Three versions of coefficients of Bernoulli polynomials: A053382/A053383; for reflected version see A196838/A196839; see also A048998 and A048999.
Sequence in context: A060480 A208682 A094673 * A295315 A089808 A290318
KEYWORD
nonn,easy,tabl,frac
AUTHOR
Wolfdieter Lang, Oct 23 2011
EXTENSIONS
Name edited by M. F. Hasler, Mar 09 2020
STATUS
approved