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%I #26 Feb 04 2022 11:07:13
%S 28,336,2100,9240,32340,96096,252252,600600,1321320,2722720,5309304,
%T 9876048,17635800,30387840,50736840,82372752,130423524,201894000,
%U 306205900,455855400,667206540,961440480,1365682500,1914330600,2650611600,3628392768,4914279216,6590029600
%N a(n) = 28*(n+1)*binomial(n+6,8)/3.
%C Number of 15-subsequences of [ 1, n ] with just 6 contiguous pairs.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F G.f.: 28*(1+2x)*x^2/(1-x)^10.
%F a(n) = C(n+1, 3)*C(n+6, 6). - _Zerinvary Lajos_, Jun 08 2005; corrected by _R. J. Mathar_, Feb 10 2016
%F From _Amiram Eldar_, Feb 04 2022: (Start)
%F Sum_{n>=2} 1/a(n) = 3*Pi^2 - 289781/9800.
%F Sum_{n>=2} (-1)^n/a(n) = 3*Pi^2/2 - 2112*log(2)/35 + 265141/9800. (End)
%t Table[28(n+1) Binomial[n+6,8]/3,{n,2,30}] (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{28,336,2100,9240,32340,96096,252252,600600,1321320,2722720},30] (* _Harvey P. Dale_, Sep 12 2017 *)
%o (PARI) a(n)=28*(n+1)*binomial(n+6,8)/3 \\ _Charles R Greathouse IV_, May 22 2013
%K nonn,easy
%O 2,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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