The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A225688 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A225688

E.g.f.: sec(x)^3+(sec(x)^2*tan(x)).
(history; published version)

#17 by Sean A. Irvine at Mon Aug 05 01:29:39 EDT 2019

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proposed

approved

#16 by Michel Marcus at Mon Aug 05 01:21:35 EDT 2019

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editing

proposed

#15 by Michel Marcus at Mon Aug 05 01:21:30 EDT 2019

REFERENCES

F. Heneghan and T. K. Petersen, Power series for up-down min-max permutations,

http://math.depaul.edu/tpeter21/MaxMinUpDownCMJ2v.pdf, 2013.

LINKS

F. Heneghan and T. K. Petersen, <a href="http://math.depaul.edu/tpeter21/MaxMinUpDownCMJ2v.pdf">Power series for up-down min-max permutations</a>, 2013.

Masato Kobayashi, <a href="https://arxiv.org/abs/1908.00701">A new refinement of Euler numbers on counting alternating permutations</a>, arXiv:1908.00701 [math.CO], 2019.

FORMULA

A225688a(n)+A225689(n) = A000111(n+2). - corrected by Vaclav Kotesovec, May 26 2013

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approved

editing

#14 by Alois P. Heinz at Fri Jun 07 07:48:59 EDT 2013

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reviewed

approved

#13 by Bruno Berselli at Fri Jun 07 03:09:53 EDT 2013

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proposed

reviewed

#12 by Vincenzo Librandi at Thu Jun 06 12:42:56 EDT 2013

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editing

proposed

#11 by Vincenzo Librandi at Thu Jun 06 12:42:44 EDT 2013

LINKS

Vincenzo Librandi, <a href="/A225688/b225688.txt">Table of n, a(n) for n = 0..200</a>

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approved

editing

#10 by Bruno Berselli at Sun May 26 17:46:53 EDT 2013

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proposed

approved

#9 by Vaclav Kotesovec at Sun May 26 16:04:07 EDT 2013

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editing

proposed

#8 by Vaclav Kotesovec at Sun May 26 16:02:27 EDT 2013

FORMULA

A225688(n)+A225689(n) = A000111(n+2). - corrected by _Vaclav Kotesovec_, May 26 2013

a(n) ~ n! * n^2*(2/Pi)^(n+3). - Vaclav Kotesovec, May 26 2013

MATHEMATICA

Table[n!*SeriesCoefficient[(1+Sin[x])/Cos[x]^3, {x, 0, n}] , {n, 0, 20}] (* Vaclav Kotesovec, May 26 2013 *)

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approved

editing