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%I #26 Feb 01 2022 09:23:13
%S 36,405,2475,10890,38610,117117,315315,772200,1750320,3719430,7482618,
%T 14360580,26453700,47006190,80901810,135326664,220641300,351511875,
%U 548358525,839188350,1261890630,1867083075,2721610125,3912807600,5553662400,7789011516,10802941380
%N a(n) = 9*(n+1)*binomial(n+2,9)/2.
%C Number of 12-subsequences of [ 1, n ] with just 2 contiguous pairs.
%H T. D. Noe, <a href="/A027782/b027782.txt">Table of n, a(n) for n = 7..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F G.f.: 9*(4+x)*x^7/(1-x)^11.
%F a(n) = binomial(n+1, 8)*binomial(n+2, 2). - _Zerinvary Lajos_, Apr 28 2005; corrected by _R. J. Mathar_, Feb 13 2016
%F From _Amiram Eldar_, Feb 01 2022: (Start)
%F Sum_{n>=7} 1/a(n) = 387341/14700 - 8*Pi^2/3.
%F Sum_{n>=7} (-1)^(n+1)/a(n) = 4*Pi^2/3 + 23552*log(2)/105 - 7435703/44100. (End)
%t Table[9*(n + 1)*Binomial[n + 2, 9]/2, {n, 7, 40}] (* _Stefan Steinerberger_, Apr 09 2006 *)
%o (Magma) [9*(n+1)*Binomial(n+2,9)/2: n in [7..33]]; // _Vincenzo Librandi_, Aug 26 2015
%K nonn,easy
%O 7,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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