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%I #30 May 07 2022 11:04:52
%S 35,350,1890,7350,23100,62370,150150,330330,675675,1301300,2382380,
%T 4176900,7054320,11531100,18314100,28352940,42902475,63596610,
%U 92534750,132382250,186486300,259008750,355077450,480957750,644245875
%N a(n) = 35*(n+1)*binomial(n+4, 7)/4.
%C Number of 12-subsequences of [ 1, n ] with just 4 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 a(n) = 35*A053347(n-3).
%F G.f.: 35*(1+x)*x^3/(1-x)^9.
%F a(n) = C(n+1, 4)*C(n+4, 4). - _Zerinvary Lajos_, May 10 2005, corrected by _R. J. Mathar_, Mar 16 2016
%F From _Amiram Eldar_, Jan 25 2022: (Start)
%F Sum_{n>=3} 1/a(n) = 5929/225 - 8*Pi^2/3.
%F Sum_{n>=3} (-1)^(n+1)/a(n) = 4*Pi^2/3 - 197/15. (End)
%t Table[35 (n + 1) Binomial[n + 4, 7]/4, {n, 3, 30}] (* or *) Table[Binomial[n + 1, 4] Binomial[n + 4, 4], {n, 3, 30}] (* _Michael De Vlieger_, Mar 16 2016 *)
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{35,350,1890,7350,23100,62370,150150,330330,675675},30] (* _Harvey P. Dale_, May 07 2022 *)
%Y Cf. A053347, A062145.
%K nonn,easy
%O 3,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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