Search: id:A002790
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%I A002790 M1559 N0608
%S A002790 1,2,6,4,30,12,84,24,90,20,132,24,5460,840,360,16,1530,
%T A002790 180,7980,840,13860,440,1656,720,81900,6552,216,112,3480,
%U A002790 240,114576,7392,117810,2380,1260,72,3838380,207480,32760
%N A002790 Denominators of Cauchy numbers of second type (= Bernoulli numbers B_n^{(n)}).
%C A002790 These coefficients (with alternating signs) are also known as the Norlund 
               [or Noerlund] numbers.
%C A002790 a(n)=(A091137=1,2,12,24,)/A000142=n! [From Paul Curtz (bpcrtz(AT)free.fr), 
               Nov 27 2008]
%D A002790 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.
%D A002790 L. M. Milne-Thompson, Calculus of Finite Differences, 1951, p. 136.
%D A002790 Guodong Liu, Some computational formulas for Norlund numbers, Fib. Quart., 
               45 (2007), 133-137.
%D A002790 N. E. Noerlund, Vorlesungen ueber Differenzenrechnung, Springer-Verlag, 
               Berlin, 1924.
%D A002790 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002790 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002790 T. D. Noe, <a href="b002790.txt">Table of n, a(n) for n=0..1000</a>
%H A002790 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%F A002790 Denominator of integral of x(x+1)...(x+n-1) from 0 to 1.
%F A002790 E.g.f.: -x/(1-x)/ln(1-x).
%F A002790 Denominator of Sum_{k=0..n} (-1)^k A008275(n,k)/(k+1). [From Peter Luschny 
               (peter(AT)luschny.de), Apr 28 2009]
%e A002790 1, 1/2, 5/6, 9/4, 251/30, 475/12, 19087/84, 36799/24, 1070017/90, ...
%p A002790 seq(denom(add((-1)^k*stirling1(n,k)/(k+1),k=0..n)),n=0..20); [From Peter 
               Luschny (peter(AT)luschny.de), Apr 28 2009]
%Y A002790 Cf. A002657. See also A002208, A002209, A002206, A002207, A006232, A006233.
%Y A002790 Sequence in context: A057643 A073039 A064538 this_sequence A108951 A108435 
               A126262
%Y A002790 Adjacent sequences: A002787 A002788 A002789 this_sequence A002791 A002792 
               A002793
%K A002790 nonn,frac,nice,easy
%O A002790 0,2
%A A002790 N. J. A. Sloane (njas(AT)research.att.com).

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