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%I #32 Jan 30 2022 04:22:11
%S 11,144,1014,5096,20475,69888,210392,572832,1436058,3359200,7407036,
%T 15519504,31097794,59907456,111435000,200880160,352023165,601277040,
%U 1003321410,1638819000,2624841765,4128783360,6386711760,9727323840,14602906500,21628990656
%N a(n) = (n+1)*binomial(n+1,11).
%C Number of 13-subsequences of [ 1, n ] with just 1 contiguous pair.
%C 1214673*a(n) is the number of permutations of (n+1) symbols that 11-commute with an (n+1)-cycle (see A233440 for definition), where 1214673 = A000757(11). - _Luis Manuel Rivera MartÃnez_, Feb 07 2014
%H T. D. Noe, <a href="/A027771/b027771.txt">Table of n, a(n) for n = 10..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_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F G.f.: (11+x)*x^10/(1-x)^13.
%F From _Amiram Eldar_, Jan 30 2022: (Start)
%F Sum_{n>=10} 1/a(n) = 11*Pi^2/6 - 57138257/3175200.
%F Sum_{n>=10} (-1)^n/a(n) = 11*Pi^2/12 + 822272*log(2)/315 - 5773608863/3175200. (End)
%t Table[(n+1)*Binomial[n+1, 11], {n, 10, 35}] (* _Amiram Eldar_, Jan 30 2022 *)
%Y Cf. A000757, A233440.
%K nonn,easy
%O 10,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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