The boustrophedon ("ox-plowing") transform
of a sequence
is given by
for
,
where
is a secant number or tangent
number defined by
![sum_(n=0)^inftyE_n(x^n)/(n!)=secx+tanx.](/images/equations/BoustrophedonTransform/NumberedEquation1.svg) |
(3)
|
The exponential generating functions of
and
are related by
![B(x)=(secx+tanx)A(x),](/images/equations/BoustrophedonTransform/NumberedEquation2.svg) |
(4)
|
where the exponential generating function is defined by
![A(x)=sum_(n=0)^inftyA_n(x^n)/(n!).](/images/equations/BoustrophedonTransform/NumberedEquation3.svg) |
(5)
|
See also
Alternating Permutation,
Entringer Number,
Secant
Number,
Seidel-Entringer-Arnold
Triangle,
Tangent Number
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References
Millar, J.; Sloane, N. J. A.; and Young, N. E. "A New Operation on Sequences: The Boustrophedon Transform." J. Combin.
Th. Ser. A 76, 44-54, 1996.Referenced on Wolfram|Alpha
Boustrophedon Transform
Cite this as:
Weisstein, Eric W. "Boustrophedon Transform."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BoustrophedonTransform.html
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