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%I #32 Feb 04 2022 11:06:07
%S 28,288,1620,6600,21780,61776,156156,360360,772200,1555840,2975544,
%T 5441904,9573720,16279200,26860680,43147632,67663332,103831200,
%U 156227500,230887800,335675340,480720240,678939300
%N a(n) = 4*(n+1)*binomial(n+2,8).
%C Number of 11-subsequences of [ 1, n ] with just 2 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.: 4*(7+2*x)*x^6/(1-x)^10.
%F a(n) = C(n+1, 7)*C(n+2, 2). - _Zerinvary Lajos_, May 13 2005
%F a(n) = 10*a(n-1)- 45*a(n-2) +120*a(n-3) -210*a(n-4) +252*a(n-5) -210*a(n-6) +120*a(n-7) -45*a(n-8) +10*a(n-9) -a(n-10). - _Harvey P. Dale_, May 20 2012
%F From _Amiram Eldar_, Feb 04 2022: (Start)
%F Sum_{n>=6} 1/a(n) = 7*Pi^2/3 - 48277/2100.
%F Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/6 + 1984*log(2)/15 - 649921/6300. (End)
%t Drop[Table[4(n+1)Binomial[n+2,8],{n,30}],5] (* or *) LinearRecurrence[ {10,-45,120,-210,252,-210,120,-45,10,-1},{28,288,1620, 6600,21780,61776, 156156,360360,772200,1555840},30] (* _Harvey P. Dale_, May 20 2012 *)
%K nonn,easy
%O 6,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
%E Offset corrected by _Harvey P. Dale_, May 20 2012
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