|
Search: id:A006233
|
|
|
| A006233 |
|
Denominators of Cauchy numbers of first type.
(Formerly M1558)
|
|
+0
13
|
|
| 1, 2, 6, 4, 30, 4, 84, 24, 90, 20, 132, 8, 5460, 840, 360, 48, 1530, 4, 1596, 168, 1980, 1320, 8280, 80, 81900, 6552, 1512, 112, 3480, 80, 114576, 7392, 117810, 7140, 1260, 8, 3838380, 5928, 936, 48, 81180
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
The signed rationals A006232(n)/a(n) provide the a-sequence for the Stirling2 Sheffer matrix A048993. See the W. Lang link concerning Sheffer a- and z-sequences.
Cauchy numbers of the first type are also called Bernoulli numbers of the second kind.
|
|
REFERENCES
|
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.
H. Jeffreys and B. S. Jeffreys, Methods of Mathematical Physics, Cambridge, 1946, p. 259.
A. Adelberg, 2-adic congruences of Norland numbers and of Bernoulli numbers of the second kind, J. Number Theory, 73 (1998), 47-58.
Ming Wu and Hao Pan, Sums of products of Bernoulli numbers of the second kind, Fib. Quart., 45 (2007), 146-150.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
W. Lang, Sheffer a- and z-sequences.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
FORMULA
|
Denominator of integral of x(x-1)...(x-n+1) from 0 to 1.
E.g.f.: x/log(1+x).
|
|
EXAMPLE
|
1, 1/2, -1/6, 1/4, -19/30, 9/4, -863/84, 1375/24, -33953/90,...
|
|
CROSSREFS
|
Cf. A006232, A002206, A002207, A002208, A002209, A002657, A002790.
Sequence in context: A106831 A038212 A039656 this_sequence A057643 A073039 A064538
Adjacent sequences: A006230 A006231 A006232 this_sequence A006234 A006235 A006236
|
|
KEYWORD
|
nonn,frac,nice,easy
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
