|
Search: id:A027642
|
|
|
| A027642 |
|
Denominator of Bernoulli number B_n. |
|
+0
33
|
|
| 1, 2, 6, 1, 30, 1, 42, 1, 30, 1, 66, 1, 2730, 1, 6, 1, 510, 1, 798, 1, 330, 1, 138, 1, 2730, 1, 6, 1, 870, 1, 14322, 1, 510, 1, 6, 1, 1919190, 1, 6, 1, 13530, 1, 1806, 1, 690, 1, 282, 1, 46410, 1, 66, 1, 1590, 1, 798, 1, 870, 1, 354, 1, 56786730, 1
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Row products of A138243. - Mats O. Granvik (mgranvik(AT)abo.fi), Mar 08 2008
|
|
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. 810.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 49.
H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 230.
Ghislain R. Franssens, On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.1.
L. M. Milne-Thompson, Calculus of Finite Differences, 1951, p. 137.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n = 0..10000
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].
K.-W. Chen, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Sequences, 4 (2001), #01.1.6.
M. Kaneko, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 3 (2000), #00.2.9.
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
Hisanori Mishima, Factorizations of many number sequences
Index entries for sequences related to Bernoulli numbers.
Index entries for "core" sequences
|
|
FORMULA
|
E.g.f: x/(e^x - 1).
|
|
EXAMPLE
|
B_n sequence begins 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, 0, -691/2730, 0, 7/6, 0, -3617/510, ...
|
|
MAPLE
|
(-1)^n*sum( (-1)^'m'*'m'!*stirling2(n, 'm')/('m'+1), 'm'=0..n);
|
|
MATHEMATICA
|
Table[ Denominator[ BernoulliB[n]], {n, 0, 68}] (from Robert G. Wilson v Oct 11 2004)
Denominator[ Range[0, 68]! CoefficientList[ Series[x/(E^x - 1), {x, 0, 68}], x]]
|
|
PROGRAM
|
(PARI) a(n)=if(n<0, 0, denominator(bernfrac(n)))
|
|
CROSSREFS
|
See A027641 for full list of references, links, formulae, etc.
Cf. also A002882, A003245, A127187, A127188.
Cf. A138243.
Adjacent sequences: A027639 A027640 A027641 this_sequence A027643 A027644 A027645
Sequence in context: A111519 A008855 A132181 this_sequence A117214 A134301 A004544
|
|
KEYWORD
|
nonn,frac,easy,core,nice
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.003 seconds
|
