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%I #27 Feb 01 2022 13:04:22
%S 45,550,3630,17160,65065,210210,600600,1555840,3719430,8314020,
%T 17551820,35271600,67897830,125847260,225544440,392251200,663966875,
%U 1096717050,1771619850,2804201400,4356527175,6652824750,9999397200,14809766400,21636143100,31208497320
%N a(n) = 5*(n+1)*binomial(n+2,10).
%C Number of 13-subsequences of [ 1, n ] with just 2 contiguous pairs.
%H T. D. Noe, <a href="/A027783/b027783.txt">Table of n, a(n) for n = 8..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F G.f.: 5*(9+2x)*x^8/(1-x)^12.
%F a(n) = C(n+1, 9)*C(n+2, 2). - _Zerinvary Lajos_, May 13 2005; corrected by _R. J. Mathar_, Mar 15 2016
%F From _Amiram Eldar_, Feb 01 2022: (Start)
%F Sum_{n>=8} 1/a(n) = 3*Pi^2 - 5218691/176400.
%F Sum_{n>=8} (-1)^n/a(n) = 3*Pi^2/2 + 13312*log(2)/35 - 49112821/176400. (End)
%t Table[5(n+1)Binomial[n+2,10],{n,8,30}] (* _Harvey P. Dale_, Jan 21 2012 *)
%K nonn,easy
%O 8,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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