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Search: id:A006233
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| A006233 |
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Denominators of Cauchy numbers of first type.
(Formerly M1558)
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+0
13
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| 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)
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OFFSET
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0,2
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COMMENT
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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.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Adelberg, 2-adic congruences of Norland numbers and of Bernoulli numbers of the second kind, J. Number Theory, 73 (1998), 47-58.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.
H. Jeffreys and B. S. Jeffreys, Methods of Mathematical Physics, Cambridge, 1946, p. 259.
Ming Wu and Hao Pan, Sums of products of Bernoulli numbers of the second kind, Fib. Quart., 45 (2007), 146-150.
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LINKS
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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.
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FORMULA
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Denominator of integral of x(x-1)...(x-n+1) from 0 to 1.
E.g.f.: x/log(1+x).
Denominator of Sum_{k=0..n} A048994(n,k)/(k+1). [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]
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EXAMPLE
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1, 1/2, -1/6, 1/4, -19/30, 9/4, -863/84, 1375/24, -33953/90,...
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MAPLE
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seq(denom(add(stirling1(n, k)/(k+1), k=0..n)), n=0..12); [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]
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CROSSREFS
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Cf. A006232, A002206, A002207, A002208, A002209, A002657, A002790.
Sequence in context: A106831 A038212 A039656 this_sequence A164020 A057643 A073039
Adjacent sequences: A006230 A006231 A006232 this_sequence A006234 A006235 A006236
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KEYWORD
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nonn,frac,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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