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%I #28 Feb 02 2022 23:48:02
%S 91,1470,12600,76160,364140,1465128,5155080,16279200,47006190,
%T 125847260,315762216,748843200,1690097500,3650610600,7582037400,
%U 15201516960,29520803025,55688330250,102301525200,183413260800,321546372840,552150337200,930092814000
%N a(n) = 7*(n+1)*binomial(n+2,14).
%C Number of 17-subsequences of [ 1, n ] with just 2 contiguous pairs.
%H T. D. Noe, <a href="/A027787/b027787.txt">Table of n, a(n) for n = 12..1000</a>
%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.: 7*(13+2x)*x^12/(1-x)^16.
%F a(n) = C(n+1, 13)*C(n+2, 2). - _Zerinvary Lajos_, May 10 2005; corrected by _R. J. Mathar_, Mar 16 2016
%F From _Amiram Eldar_, Feb 01 2022: (Start)
%F Sum_{n>=12} 1/a(n) = 13*Pi^2/3 - 106775635663/2497294800.
%F Sum_{n>=12} (-1)^n/a(n) = 13*Pi^2/6 + 12132352*log(2)/3465 - 6114275457217/2497294800. (End)
%t Table[7(n+1)Binomial[n+2,14],{n,12,40}] (* _Harvey P. Dale_, Jul 18 2011 *)
%K nonn,easy
%O 12,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
%E Offset corrected by _Harvey P. Dale_, Jul 18 2011
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