|
%I #23 Feb 01 2022 08:51:58
%S 84,960,5940,26400,94380,288288,780780,1921920,4375800,9335040,
%T 18845112,36279360,67016040,119380800,205931880,345181056,563861100,
%U 899870400,1406047500,2154952800,3244861620,4807202400,7015706100,10097568000,14346961200,20141282304
%N a(n) = 12*(n+1)*binomial(n+3,9).
%C Number of 13-subsequences of [ 1, n ] with just 3 contiguous pairs.
%H T. D. Noe, <a href="/A027794/b027794.txt">Table of n, a(n) for n = 6..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.: 12*(7+3x)*x^6/(1-x)^11.
%F a(n) = C(n+1, 7)*C(n+3, 3) - _Zerinvary Lajos_, May 10 2005; corrected by _R. J. Mathar_, Mar 16 2016
%F From _Amiram Eldar_, Feb 01 2022: (Start)
%F Sum_{n>=6} 1/a(n) = 7*Pi^2/2 - 386741/11200.
%F Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/4 + 512*log(2)/5 - 2964833/33600. (End)
%t Table[12 (n + 1) Binomial[n + 3, 9], {n, 6, 31}] (* or *) Table[Binomial[n + 1, 7] Binomial[n + 3, 3], {n, 6, 31}] (* _Michael De Vlieger_, Mar 16 2016 *)
%K nonn,easy
%O 6,1
%A Thi Ngoc Dinh (via _R. K. Guy_)
|
