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%I #25 Jan 30 2022 04:23:32
%S 16,289,2754,18411,96900,427329,1641486,5638611,17651304,51074375,
%T 138105110,352023165,851809140,1968053535,4362680250,9316746045,
%U 19234572480,38504502630,74934688620,142097513250,263083395960,476403662790,845119028340,1470739178610
%N a(n) = (n+1)*binomial(n+1,16).
%C Number of 18-subsequences of [ 1, n ] with just 1 contiguous pair.
%H T. D. Noe, <a href="/A027776/b027776.txt">Table of n, a(n) for n = 15..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_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
%F G.f.: (16+x)*x^15/(1-x)^18.
%F From _Amiram Eldar_, Jan 30 2022: (Start)
%F Sum_{n>=15} 1/a(n) = 107074439839/4058104050 - 8*Pi^2/3.
%F Sum_{n>=15} (-1)^(n+1)/a(n) = 4*Pi^2/3 + 684654592*log(2)/9009 - 30545942365399/579729150. (End)
%t Table[(n + 1) Binomial[n + 1, 16], {n, 15, 100}] (* _T. D. Noe_, Mar 28 2012 *)
%K nonn,easy
%O 15,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
%E Incorrect formula deleted. - _R. J. Mathar_, Feb 13 2016
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