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%I #21 Feb 04 2022 09:27:26
%S 70,756,4410,18480,62370,180180,462462,1081080,2342340,4764760,
%T 9189180,16930368,29980860,51279480,85058820,137287920,216228474,
%U 333125100,503052550,745945200,1087836750,1562340780,2212405650,3092380200,4270429800,5831345520,7879792536
%N a(n) = 14*(n+1)*binomial(n+4,8).
%C Number of 13-subsequences of [ 1, n ] with just 4 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.: 14*(5+4x)*x^4/(1-x)^10.
%F a(n) = C(n+1, 5)*C(n+4, 4). - _Zerinvary Lajos_, May 10 2005; corrected by _R. J. Mathar_, Feb 10 2016
%F From _Amiram Eldar_, Feb 04 2022: (Start)
%F Sum_{n>=4} 1/a(n) = 10*Pi^2/3 - 145013/4410.
%F Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/3 + 128*log(2)/7 - 42793/1470. (End)
%t Table[14 * (n+1) * Binomial[n+4, 8], {n, 4, 50}] (* _Amiram Eldar_, Feb 04 2022 *)
%K nonn,easy
%O 4,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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