%I #35 Jan 30 2022 04:17:28
%S 5,36,147,448,1134,2520,5082,9504,16731,28028,45045,69888,105196,
%T 154224,220932,310080,427329,579348,773927,1020096,1328250,1710280,
%U 2179710,2751840,3443895,4275180,5267241,6444032,7832088,9460704,11362120,13571712,16128189
%N a(n) = (n+1)*binomial(n+1,5).
%C Number of 7-subsequences of [ 1, n ] with just 1 contiguous pair.
%C 8*a(n) is the number of permutations of (n+1) symbols that 5-commute with an (n+1)-cycle (see A233440 for definition), where 8 = A000757(5). - _Luis Manuel Rivera MartÃnez_, Feb 07 2014
%H Vincenzo Librandi, <a href="/A027765/b027765.txt">Table of n, a(n) for n = 4..1000</a>
%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%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 G.f.: (5+x)*x^4/(1-x)^7.
%F From _Amiram Eldar_, Jan 30 2022: (Start)
%F Sum_{n>=4} 1/a(n) = 5*Pi^2/6 - 575/72.
%F Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/12 + 160*log(2)/3 - 2945/72. (End)
%p a:=n->(sum((numbcomp(n,6)), j=2..n)):seq(a(n), n=6..34); # _Zerinvary Lajos_, Aug 26 2008
%t Table[(n+1)Binomial[n+1,5],{n,4,40}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{5,36,147,448,1134,2520,5082},40] (* _Harvey P. Dale_, Jan 15 2017 *)
%o (Magma) [(n+1)*Binomial(n+1,5): n in [4..40]]; // _Vincenzo Librandi_, Aug 09 2017
%Y Cf. A000757, A233440.
%K nonn,easy
%O 4,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
%E Incorrect formula deleted by _R. J. Mathar_, Feb 13 2016