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%I #34 Jan 30 2022 04:24:14
%S 6,49,224,756,2100,5082,11088,22308,42042,75075,128128,210392,334152,
%T 515508,775200,1139544,1641486,2321781,3230304,4427500,5985980,
%U 7992270,10548720,13775580,17813250,22824711,28998144,36549744,45726736,56810600,70120512,86017008
%N a(n) = (n+1)*binomial(n+1,6).
%C Number of 8-subsequences of [ 1, n ] with just 1 contiguous pair.
%C 36*a(n) is the number of permutations of (n+1) symbols that 6-commute with an (n+1)-cycle (see A233440 for definition), where 36 = A000757(6). - _Luis Manuel Rivera MartÃnez_, Feb 07 2014
%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_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F G.f.: (6+x)*x^5/(1-x)^8.
%F From _Amiram Eldar_, Jan 30 2022: (Start)
%F Sum_{n>=5} 1/a(n) = 3019/300 - Pi^2.
%F Sum_{n>=5} (-1)^(n+1)/a(n) = Pi^2/2 + 512*log(2)/5 - 22729/300. (End)
%Y Cf. A000757, A233440.
%K nonn,easy
%O 5,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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