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Search: id:A002657
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| A002657 |
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Numerators of Cauchy numbers of second type (= Bernoulli numbers B_n^{(n)}).
(Formerly M3790 N1545)
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+0
11
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| 1, 1, 5, 9, 251, 475, 19087, 36799, 1070017, 2082753, 134211265, 262747265, 703604254357, 1382741929621, 8164168737599, 5362709743125, 8092989203533249, 15980174332775873, 12600467236042756559
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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These coefficients (with alternating signs) are also known as the Norlund [or Noerlund] numbers.
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.
L. M. Milne-Thompson, Calculus of Finite Differences, 1951, p. 136.
Guodong Liu, Some computational formulas for Norlund numbers, Fib. Quart., 45 (2007), 133-137.
N. E. Noerlund, Vorlesungen ueber Differenzenrechnung, Springer-Verlag, Berlin, 1924.
P. Curtz Integration numerique des systemes differentiels .., C.C.S.A.,Arcueil,1969. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 24 2008]
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
Index entries for sequences related to Bernoulli numbers.
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FORMULA
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Numerator of integral of x(x+1)...(x+n-1) from 0 to 1.
E.g.f.: -x/(1-x)/ln(1-x).
Numerator of Sum_{k=0..n} (-1)^(n-k) A008275(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, 5/6, 9/4, 251/30, 475/12, 19087/84, 36799/24, 1070017/90, ...
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MAPLE
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seq(numer(add((-1)^(n-k)*stirling1(n, k)/(k+1), k=0..n)), n=0..10); [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]
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CROSSREFS
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Cf. A002790. See also A002208, A002209, A002206, A002207, A006232, A006233.
Sequence in context: A097397 A092584 A145400 this_sequence A046093 A097086 A109076
Adjacent sequences: A002654 A002655 A002656 this_sequence A002658 A002659 A002660
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KEYWORD
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nonn,frac,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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