The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A211606 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A211606

Total number of inversions over all involutions of length n.
(history; published version)

#47 by Alois P. Heinz at Sun Aug 30 13:00:32 EDT 2020

STATUS

editing

approved

#46 by Alois P. Heinz at Sun Aug 30 13:00:28 EDT 2020

FORMULA

a(n) = a(n-1) + (n-1)*a(n-2) + A000085(n-2)*(n-1)^2 for n>1; a(0) = a(1) = 0.

#45 by Alois P. Heinz at Sun Aug 30 13:00:02 EDT 2020

CROSSREFS

Cf. A000085, A001809, A161124, A216239, A337193.

STATUS

approved

editing

#44 by Michael Somos at Mon Jun 03 19:12:53 EDT 2019

STATUS

editing

approved

#43 by Michael Somos at Mon Jun 03 19:12:35 EDT 2019

DATA

0, 0, 1, 5, 26, 110, 490, 2086, 9240, 40776, 185820, 855580, 4048616, 19455800, 95773496, 479581480, 2454041920, 12776826816, 67849286160, 366455145936, 2015621873440, 11268605368160, 64074235576736, 370040657037920, 2171138049287296, 12928631894588800, 78139702237771200

MATHEMATICA

(* first do *) Needs["Combinatorica`"] // Quiet (* then *)

Table[Total[Map[Inversions, Involutions[n]]], {n, 0, 10}]

a[ n_] := If[ n < 0, 0, n! SeriesCoefficient[ (x^2/2 + x^3/3 + x^4/4) Exp[x + x^2/2], {x, 0, n}]]; (* Michael Somos, Jun 03 2019 *)

PROG

(PARI) {a(n) = if( n<0, 0, n! * polcoeff( (x^2/2 + x^3/3 + x^4/4) * exp(x + x^2/2 + x * O(x^n)), n))}; /* Michael Somos, Jun 03 2019 */

STATUS

approved

editing

Discussion

Mon Jun 03

19:12

Michael Somos: Added more info.

#42 by OEIS Server at Sun Feb 28 17:29:52 EST 2016

LINKS

Alois P. Heinz, <a href="/A211606/b211606_1.txt">Table of n, a(n) for n = 0..800</a>

#41 by Alois P. Heinz at Sun Feb 28 17:29:52 EST 2016

STATUS

editing

approved

Discussion

Sun Feb 28

17:29

OEIS Server: Installed new b-file as b211606.txt.  Old b-file is now b211606_1.txt.

#40 by Alois P. Heinz at Sun Feb 28 17:29:49 EST 2016

LINKS

Alois P. Heinz, <a href="/A211606/b211606_1.txt">Table of n, a(n) for n = 0..300800</a>

STATUS

approved

editing

#39 by Joerg Arndt at Thu Aug 15 04:39:44 EDT 2013

STATUS

proposed

approved

#38 by Vaclav Kotesovec at Thu Aug 15 03:50:22 EDT 2013

STATUS

editing

proposed