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%I #29 Feb 04 2022 07:43:28
%S 21,196,1008,3780,11550,30492,72072,156156,315315,600600,1089088,
%T 1893528,3174444,5155080,8139600,12534984,18877089,27861372,40378800,
%U 57557500,80810730,111891780,152956440,206633700,276105375,365195376,478469376,621345648,800217880
%N a(n) = 7*(n+1)*binomial(n+2,7)/2.
%C Number of 10-subsequences of [ 1, n ] with just 2 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*(3+x)*x^5/(1-x)^9.
%F a(n) = C(n+1, 6)*C(n+2, 2). - _Zerinvary Lajos_, Apr 28 2005; corrected by _R. J. Mathar_, Feb 10 2016
%F From _Amiram Eldar_, Feb 04 2022: (Start)
%F Sum_{n>=5} 1/a(n) = 2969/150 - 2*Pi^2.
%F Sum_{n>=5} (-1)^(n+1)/a(n) = Pi^2 + 384*log(2)/5 - 3153/50. (End)
%t Table[7(n+1) Binomial[n+2,7]/2,{n,5,30}] (* _Harvey P. Dale_, Feb 25 2013 *)
%o (PARI) a(n)=7*(n+1)*binomial(n+2,7)/2 \\ _Charles R Greathouse IV_, Feb 26 2013
%K nonn,easy
%O 5,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
%E Offset corrected by _Harvey P. Dale_, Feb 26 2013
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