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%I #18 Feb 03 2022 05:26:28
%S 210,2640,17820,85800,330330,1081080,3123120,8168160,19691100,
%T 44341440,94225560,190466640,368588220,686439600,1235591280,
%U 2157381600,3665097150,6074125200,9842332500,15623407800,24336462150,37255818600,56125648800,83304936000,121949170200
%N a(n) = 30*(n+1)*binomial(n+4,10).
%C Number of 15-subsequences of [ 1, n ] with just 4 contiguous pairs.
%H T. D. Noe, <a href="/A027806/b027806.txt">Table of n, a(n) for n = 6..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.: 30*(7+4x)*x^6/(1-x)^12.
%F a(n) = C(n+1, 7)*C(n+4, 4). - _Zerinvary Lajos_, May 26 2005; corrected by _R. J. Mathar_, Feb 13 2016
%F From _Amiram Eldar_, Feb 03 2022: (Start)
%F Sum_{n>=6} 1/a(n) = 14*Pi^2/3 - 10444807/226800.
%F Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/3 + 3584*log(2)/45 - 2534651/32400. (End)
%t Table[30 * (n+1) * Binomial[n+4, 10], {n, 6, 50}] (* _Amiram Eldar_, Feb 03 2022 *)
%K nonn,easy
%O 6,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
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