The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A355488 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A355488

Expansion of g.f. f/(1+2*f) where f is the g.f. of nonempty permutations.
(history; published version)

#34 by Peter Luschny at Tue Apr 25 10:44:20 EDT 2023

STATUS

proposed

approved

#33 by F. Chapoton at Mon Apr 24 15:08:06 EDT 2023

STATUS

editing

proposed

#32 by F. Chapoton at Mon Apr 24 15:07:44 EDT 2023

CROSSREFS

Cf. A000108, A003319, A000957, A000142, A052186, A126984, A059438, A122827.

STATUS

approved

editing

Discussion

Mon Apr 24

15:08

F. Chapoton: adding one cross-reference (similar sequence)

#31 by Michael De Vlieger at Sat Sep 10 14:02:09 EDT 2022

STATUS

proposed

approved

#30 by Peter Luschny at Sat Sep 10 11:12:25 EDT 2022

STATUS

editing

proposed

#29 by Peter Luschny at Sat Sep 10 11:07:48 EDT 2022

LINKS

David Callan, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Callan/callan91.html">Counting Stabilized-Interval-Free Permutations</a>, Journal of Integer Sequences, Vol. 7 (2004), Article 04.1.8.

FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000056">The number of connected components of a permutation.</a>

#28 by Peter Luschny at Sat Sep 10 10:59:51 EDT 2022

COMMENTS

a(n) is the number of permutations of [n] whose number of components is odd minus the number of those permutations with an even number of components. - Peter Luschny, Sep 10 2022

EXAMPLE

Consider the permutations of [3]: [2,3,1], [3,1,2] and [3,2,1] have 1 component,

[1,3,2] and [2,1,3] have 2 components, and [1,2,3] has three components. Thus 3 - 2 + 1 = 2 = a(3). - Peter Luschny, Sep 10 2022

#27 by Peter Luschny at Sat Sep 10 09:53:33 EDT 2022

FORMULA

a(n) = -Sum_{k=1..n} (-1)^k * A059438(n, k) for n >= 1. - Peter Luschny, Sep 10 2022

#26 by Peter Luschny at Sat Sep 10 09:47:49 EDT 2022

FORMULA

a(n) = -Sum_{1..n} (-1)^k * A059438(n, k) for n >= 1. _- _Peter Luschny_, Sep 10 2022

#25 by Peter Luschny at Sat Sep 10 09:47:12 EDT 2022

FORMULA

a(n) = -Sum_{1..n} (-1)^k * A059438(n, k) for n >= 1. Peter Luschny, Sep 10 2022