A number defined by Bernoulli
polynomial of the second kind (Roman 1984, p. 294), also called Cauchy numbers
of the first kind. The first few for A006232
and A006233 ). They are given by
where falling factorial , and have exponential
generating function
See also Bernoulli Number ,
Bernoulli
Polynomial of the Second Kind
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References Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Jeffreys, H. and Jeffreys, B. S.
Methods
of Mathematical Physics, 3rd ed. Roman, S. The
Umbral Calculus. Sloane,
N. J. A. Sequences A006232 /M5067
and A006233 /M1558 in "The On-Line Encyclopedia
of Integer Sequences." Referenced on Wolfram|Alpha Bernoulli Number of the
Second Kind
Cite this as:
Weisstein, Eric W. "Bernoulli Number of the Second Kind." From MathWorld https://mathworld.wolfram.com/BernoulliNumberoftheSecondKind.html
Subject classifications
, where 
is a Bernoulli
polynomial of the second kind (Roman 1984, p. 294), also called Cauchy numbers
of the first kind. The first few for 
, 1, 2, ... are 1, 1/2, 
, 1/4, 
, 9/4, ... (OEIS A006232
and A006233). They are given by
is a falling factorial, and have exponential
generating function
