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%I #23 Feb 04 2022 09:04:05
%S 35,336,1764,6720,20790,55440,132132,288288,585585,1121120,2042040,
%T 3564288,5996172,9767520,15465240,23876160,36038079,53300016,77392700,
%U 110510400,155405250,215495280,294987420,399016800,533803725,706829760,927034416,1205033984,1553364120
%N a(n) = 7*(n+1)*binomial(n+3,7).
%C Number of 11-subsequences of [ 1, n ] with just 3 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 G.f.: 7*(5+3x)*x^4/(1-x)^9.
%F a(n) = C(n+1, 5)*C(n+3, 3). - _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) = 5*Pi^2/2 - 2957/120.
%F Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/4 + 32*log(2) - 4139/120. (End)
%t Table[7(n+1)Binomial[n+3,7],{n,4,30}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{35,336,1764,6720,20790,55440,132132,288288,585585},30] (* _Harvey P. Dale_, Jan 04 2015 *)
%K nonn,easy
%O 4,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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