login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053383 Triangle T(n,k) giving denominator of coefficient of x^(n-k) in Bernoulli polynomial B(n, x), n >= 0, 0<=k<=n. 23
1, 1, 2, 1, 1, 6, 1, 2, 2, 1, 1, 1, 1, 1, 30, 1, 2, 3, 1, 6, 1, 1, 1, 2, 1, 2, 1, 42, 1, 2, 2, 1, 6, 1, 6, 1, 1, 1, 3, 1, 3, 1, 3, 1, 30, 1, 2, 1, 1, 5, 1, 1, 1, 10, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 66, 1, 2, 6, 1, 1, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2730, 1, 2, 1, 1, 6, 1, 7, 1, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 809.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 48, [14a].

M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 53.

H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.

LINKS

T. D. Noe, Rows n=0..50 of triangle, flattened

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

D. H. Lehmer, A new approach to Bernoulli polynomials, The American mathematical monthly 95.10 (1988): 905-911.

Index entries for sequences related to Bernoulli numbers.

EXAMPLE

The polynomials B(0,x), B(1,x), B(2,x), ... are 1; x-1/2; x^2-x+1/6; x^3-3/2*x^2+1/2*x; x^4-2*x^3+x^2-1/30; x^5-5/2*x^4+5/3*x^3-1/6*x; x^6-3*x^5+5/2*x^4-1/2*x^2+1/42; ...

Triangle A053382/A053383 begins:

1,

1, -1/2,

1, -1, 1/6,

1, -3/2, 1/2, 0,

1, -2, 1, 0, -1/30,

1, -5/2, 5/3, 0, -1/6, 0,

1, -3, 5/2, 0, -1/2, 0, 1/42,

...

Triangle A196838/A196839 begins (this is the reflected version):

1,

-1/2, 1,

1/6, -1, 1,

0, 1/2, -3/2, 1,

-1/30, 0, 1, -2, 1,

0, -1/6, 0, 5/3, -5/2, 1,

1/42, 0, -1/2, 0, 5/2, -3, 1,

...

MAPLE

with(numtheory); bernoulli(n, x);

MATHEMATICA

t[n_, k_] := Denominator[ Coefficient[ BernoulliB[n, x], x, n - k]]; Flatten[ Table[t[n, k], {n, 0, 13}, {k, 0, n}]] (* Jean-Fran├žois Alcover, Jan 15 2013 *)

PROG

(PARI) v=[]; for(n=0, 6, v=concat(v, apply(denominator, Vec(bernpol(n))))); v \\ Charles R Greathouse IV, Jun 08 2012

CROSSREFS

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

Cf. A144845 (lcm of row n)

Sequence in context: A216919 A152656 A096162 * A181538 A125731 A123361

Adjacent sequences:  A053380 A053381 A053382 * A053384 A053385 A053386

KEYWORD

nonn,easy,nice,frac,tabl

AUTHOR

N. J. A. Sloane, Jan 06 2000

EXTENSIONS

More terms from James A. Sellers, Jan 10 2000

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 20 10:20 EDT 2018. Contains 313915 sequences. (Running on oeis4.)