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Number of words of length 6 in the n(n-1)/2 transpositions of S[ n ] equivalent to the identity.
1

%I #18 Sep 08 2022 08:44:50

%S 0,1,243,3936,20860,72315,197421,460768,961416,1843245,3306655,

%T 5621616,9142068,14321671,21730905,32075520,46216336,65190393,

%U 90233451,122803840,164607660,217625331,284139493,366764256,468475800,592644325,743067351,924004368

%N Number of words of length 6 in the n(n-1)/2 transpositions of S[ n ] equivalent to the identity.

%H Vincenzo Librandi, <a href="/A029700/b029700.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = n*(n-1)*(15*n^4 + 30*n^3 - 105*n^2 - 700*n + 1344)/8.

%F G.f.: -x^2*(481*x^4 - 1624*x^3 + 2256*x^2 + 236*x + 1) / (x-1)^7. - _Colin Barker_, May 28 2015

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,243,3936,20860,72315,197421},30] (* _Harvey P. Dale_, Mar 27 2022 *)

%o (Magma) [n*(n-1)*(15*n^4+30*n^3-105*n^2-700*n+1344)/8: n in [1..45]]; // _Vincenzo Librandi_, Jun 30 2011

%o (PARI) concat(0, Vec(-x^2*(481*x^4-1624*x^3+2256*x^2+236*x+1) / (x-1)^7 + O(x^100))) \\ _Colin Barker_, May 28 2015

%K nonn,easy

%O 1,3

%A Paolo Dominici (pl.dm(AT)libero.it)

%E a(1) corrected by _Vincenzo Librandi_, Jun 30 2011