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%I #26 Feb 20 2023 03:14:54
%S 10,252,736,1462,2430,3640,5092,6786,8722,10900,13320,15982,18886,
%T 22032,25420,29050,32922,37036,41392,45990,50830,55912,61236,66802,
%U 72610,78660,84952,91486,98262,105280,112540,120042,127786,135772,144000,152470,161182
%N a(n) = (11n+1)*(11n+10).
%H T. D. Noe, <a href="/A001536/b001536.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 242*n + a(n-1) with a(0)=10. - _Vincenzo Librandi_, Nov 12 2010
%F G.f.: -2*(5+111*x+5*x^2)/(x-1)^3 . - _R. J. Mathar_, May 30 2022
%F From _Amiram Eldar_, Feb 20 2023: (Start)
%F a(n) = A017401(n)*A017509(n).
%F Sum_{n>=0} 1/a(n) = cot(Pi/11)*Pi/99.
%F Product_{n>=0} (1 - 1/a(n)) = cosec(Pi/11)*cos(sqrt(85)*Pi/22).
%F Product_{n>=0} (1 + 1/a(n)) = cosec(Pi/11)*cos(sqrt(77)*Pi/22). (End)
%t Table[(11*n + 1)*(11*n + 10), {n, 0, 40}] (* _Amiram Eldar_, Feb 20 2023 *)
%o (PARI) a(n)=(11*n+1)*(11*n+10) \\ _Charles R Greathouse IV_, Jun 16 2017
%Y Cf. A017401, A017509.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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