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A196839 Triangle of denominators of the coefficient of of x^m in the n-th Bernoulli polynomial, 0 <= m <= n. 20
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The numerator triangle is found under A196838.

This is the row reversed triangle A053383.

LINKS

Table of n, a(n) for n=0..83.

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.

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

Adjacent sequences:  A196836 A196837 A196838 * A196840 A196841 A196842

KEYWORD

nonn,easy,tabl,frac

AUTHOR

Wolfdieter Lang, Oct 23 2011

EXTENSIONS

Name edited by M. F. Hasler, Mar 09 2020

STATUS

approved

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Last modified March 31 16:44 EDT 2020. Contains 333151 sequences. (Running on oeis4.)