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%I
%S 14,225,1920,11560,55080,220932,775200,2441880,7034940,18795370,
%T 47070144,111435000,251100200,541574100,1123264800,2249204040,
%U 4362680250,8220658275,15085939200,27020703600,47327171760,81198579000,136666699200,225962211600,367443055800
%N a(n) = (n+1)*binomial(n+1,14).
%C Number of 16-subsequences of [ 1, n ] with just 1 contiguous pair.
%H T. D. Noe, <a href="/A027774/b027774.txt">Table of n, a(n) for n = 13..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_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F G.f.: (14+x)*x^13/(1-x)^16.
%F From _Amiram Eldar_, Jan 30 2022: (Start)
%F Sum_{n>=13} 1/a(n) = 107159834863/4637833200 - 7*Pi^2/3.
%F Sum_{n>=13} (-1)^(n+1)/a(n) = 7*Pi^2/6 + 125673472*log(2)/6435 - 62835162326017/4637833200. (End)
%t Table[(n+1)Binomial[n+1,14],{n,13,40}] (* _Harvey P. Dale_, Nov 04 2017 *)
%K nonn,easy
%O 13,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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