%I M4018 N1666 #29 Sep 08 2022 08:44:27
%S 5,61,479,3111,18270,101166,540242,2819266,14494859,73802835,
%T 373398489,1881341265,9453340172,47417364268,237571096820,
%U 1189405165908,5951965440609,29775517732665,148927275340835,744793282001995
%N Number of permutations of [n] with exactly 2 increasing runs of length at least 2.
%D F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A000363/b000363.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (14,-75,196,-263,174,-45).
%F a(n) = (5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16. - _Vaclav Kotesovec_, Nov 19 2012
%F G.f.: -x^4*(9*x-5)/((x-1)^3*(3*x-1)^2*(5*x-1)). - _Vaclav Kotesovec_, Nov 19 2012
%t Table[(5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16,{n,4,20}] (* _Vaclav Kotesovec_, Nov 19 2012 *)
%o (Magma) [(5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16: n in [4..30]]; // _Vincenzo Librandi_, May 03 2013
%Y Contribution from _Johannes W. Meijer_, May 24 2009: (Start)
%Y The a(n) sequence equals the third left hand column of A008971.
%Y The a(2*n) sequence equals the third left hand column of A160486.
%Y (End)
%K nonn,easy
%O 4,1
%A _N. J. A. Sloane_
%E More terms and better definition from _Jon E. Schoenfield_, Mar 25 2010