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%I #17 Feb 03 2022 04:53:22
%S 7,84,504,2100,6930,19404,48048,108108,225225,440440,816816,1447992,
%T 2469012,4069800,6511680,10147368,15444891,23015916,33649000,48348300,
%U 68378310,95315220,131105520,178132500,239291325,318073392,418660704,546031024,706074600,905723280
%N a(n) = 7*(n+1)*binomial(n+6,7)/2.
%C Number of 14-subsequences of [ 1, n ] with just 6 contiguous pairs.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n) = 7*A052181(n).
%F G.f.: 7*(1+3*x)*x/(1-x)^9.
%F a(n) = C(n+1,2)*C(n+6,6). - _Zerinvary Lajos_, May 26 2005
%F From _Amiram Eldar_, Feb 03 2022: (Start)
%F Sum_{n>=1} 1/a(n) = 5969/300 - 2*Pi^2.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2 - 384*log(2)/5 + 13049/300. (End)
%t Table[7*(n + 1)*Binomial[n + 6, 7]/2, {n, 1, 50}] (* _Amiram Eldar_, Feb 03 2022 *)
%Y Cf. A052181.
%K nonn,easy
%O 1,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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