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%I #36 Jan 28 2022 03:58:13
%S 6,40,150,420,980,2016,3780,6600,10890,17160,26026,38220,54600,76160,
%T 104040,139536,184110,239400,307230,389620,488796,607200,747500,
%U 912600,1105650,1330056,1589490,1887900,2229520,2618880,3060816,3560480,4123350,4755240,5462310
%N a(n) = 2*(n+1)*binomial(n+2,4).
%C Number of 7-subsequences of [ 1, n ] with just 2 contiguous pairs.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: 2*(3+2x)*x^2/(1-x)^6.
%F a(n) = 2*A006411(n+1).
%F a(n) = C(n+1, 3)*C(n+2, 2) - _Zerinvary Lajos_, May 13 2005, corrected by _R. J. Mathar_, Feb 13 2016
%F From _Amiram Eldar_, Jan 28 2022: (Start)
%F Sum_{n>=2} 1/a(n) = Pi^2 - 29/3.
%F Sum_{n>=2} (-1)^n/a(n) = Pi^2/2 + 8*log(2) - 31/3. (End)
%t Table[2(n+1)Binomial[n+2,4],{n,2,35}] (* _Harvey P. Dale_, Feb 03 2011 *)
%Y Equals second right hand column of A163934. - _Johannes W. Meijer_, Oct 16 2009
%Y Cf. A006411.
%K nonn,easy
%O 2,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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