The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A193778

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A193778

Number of signed permutations of length 2n invariant under D and D'bar.
(history; published version)

#36 by Michael De Vlieger at Mon Oct 07 20:27:32 EDT 2024

STATUS

proposed

approved

#35 by Andrew Howroyd at Mon Oct 07 19:49:02 EDT 2024

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editing

proposed

#34 by Andrew Howroyd at Mon Oct 07 19:40:39 EDT 2024

CROSSREFS

Column k=4 of A376826.

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approved

editing

#33 by Joerg Arndt at Sun May 30 03:33:21 EDT 2021

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reviewed

approved

#32 by Michel Marcus at Sun May 30 03:28:43 EDT 2021

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proposed

reviewed

#31 by Michel Marcus at Sun May 30 03:28:36 EDT 2021

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editing

proposed

#30 by Michel Marcus at Sun May 30 03:28:28 EDT 2021

LINKS

Andy Hardt, and Justin M. Troyka, <a href="http://puma.dimai.unifi.it/23_3/hardt_troyka.pdf">Restricted Symmetric Signed Permutations</a>, Department of Mathematics, Carleton College, 2013.

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reviewed

editing

#29 by Joerg Arndt at Sun May 30 02:58:46 EDT 2021

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proposed

reviewed

#28 by Peter Luschny at Sun May 30 02:35:44 EDT 2021

STATUS

editing

proposed

#27 by Peter Luschny at Sun May 30 02:03:35 EDT 2021

FORMULA

From Peter Luschny, May 30 2021: (Start)

a(n) = 2^n * hypergeom([-n/2, (1 - n)/2], [], 2).

a(n) = 2^n * A000085(n).

a(n) = n! * [x^n] exp(2*x*(x + 1)). (End)

MAPLE

exp(2*x*(x + 1)): series(%, x, 23):

seq(n!*coeff(%, x, n), n = 0..22); # Peter Luschny, May 30 2021

MATHEMATICA

a[n_] := 2^n HypergeometricPFQ[{-n/2, (1-n)/2}, {}, 2];

Table[a[n], {n, 0, 22}] (* Peter Luschny, May 30 2021 *)

CROSSREFS

Cf. A193777, A000085.

STATUS

approved

editing