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%I #29 Jan 30 2022 04:17:20
%S 9,100,605,2640,9295,28028,75075,183040,413270,875160,1755182,3359200,
%T 6172530,10943240,18795370,31380096,51074375,81238300,126544275,
%U 193393200,290435145,429214500,624962325,897561600,1272714300,1783342704,2471261100,3389158080
%N a(n) = (n+1)*binomial(n+1, 9).
%C Number of 11-subsequences of [ 1, n ] with just 1 contiguous pair.
%C 13208*a(n) is the number of permutations of (n+1) symbols that 9-commute with an (n+1)-cycle (see A233440 for definition), where 13208=A000757(9). - _Luis Manuel Rivera MartÃnez_, Feb 06 2014
%H T. D. Noe, <a href="/A027769/b027769.txt">Table of n, a(n) for n = 8..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_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F G.f.: (9+x)*x^8/(1-x)^11.
%F From _Amiram Eldar_, Jan 30 2022: (Start)
%F Sum_{n>=8} 1/a(n) = 3*Pi^2/2 - 575499/39200.
%F Sum_{n>=8} (-1)^n/a(n) = 3*Pi^2/4 + 24576*log(2)/35 - 19365109/39200. (End)
%t Table[(n+1)*Binomial[n+1, 9], {n, 8, 35}] (* _Amiram Eldar_, Jan 30 2022 *)
%Y Cf. A000757, A233440.
%K nonn
%O 8,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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