|
| |
|
|
A053383
|
|
Triangle T(n,k) giving denominator of coefficient of x^(n-k) in Bernoulli polynomial B(n, x), n >= 0, 0<=k<=n.
|
|
13
|
|
|
|
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].
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].
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; ...
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, ... = A053382/A053383 (reflected)
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, ... = A053382/A053383
|
|
|
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-François 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
|
Cf. A053382, A048998, 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
|
| |
|
|
