|
Search: id:A053383
|
|
|
| A053383 |
|
Triangle T(n,k) giving denominator of coefficient of x^(n-k) in Bernoulli polynomial B(n, x), n >= 0, 0<=k<=n. |
|
+0
3
|
|
| 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; listen)
|
|
|
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
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 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);
|
|
CROSSREFS
|
Cf. A053382, A048998, A048999.
Sequence in context: A139622 A139547 A096162 this_sequence A125731 A123361 A107106
Adjacent sequences: A053380 A053381 A053382 this_sequence A053384 A053385 A053386
|
|
KEYWORD
|
nonn,easy,nice,frac,tabl
|
|
AUTHOR
|
njas, Jan 06 2000
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 10 2000
|
|
|
Search completed in 0.002 seconds
|
