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%I #20 Feb 03 2022 05:22:12
%S 84,1050,6930,32340,120120,378378,1051050,2642640,6126120,13273260,
%T 27159132,52907400,98760480,177578940,308897820,521694096,858049500,
%U 1377926550,2165313150,3336032700,5047562520,7511253750,11007400950,15903669600,22677454800,31942814904
%N a(n) = 21*(n+1)*binomial(n+6,9).
%C Number of 16-subsequences of [ 1, n ] with just 6 contiguous pairs.
%H T. D. Noe, <a href="/A027821/b027821.txt">Table of n, a(n) for n = 3..1000</a>
%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.: 42*(2+3x)*x^3/(1-x)^11.
%F a(n) = C(n+1, 4)*C(n+6, 6). - _Zerinvary Lajos_, Jun 08 2005; corrected by _R. J. Mathar_, Feb 13 2016
%F From _Amiram Eldar_, Feb 03 2022: (Start)
%F Sum_{n>=3} 1/a(n) = 1161049/29400 - 4*Pi^2.
%F Sum_{n>=3} (-1)^(n+1)/a(n) = 2*Pi^2 - 1536*log(2)/35 + 104773/9800. (End)
%t LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{84,1050,6930,32340,120120,378378,1051050,2642640,6126120,13273260,27159132},30] (* _Harvey P. Dale_, Jul 07 2016 *)
%K nonn,easy
%O 3,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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