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%I #18 Sep 21 2023 01:45:07
%S 0,15,28,135,132,455,360,1071,760,2079,1380,3575,2268,5655,3472,8415,
%T 5040,11951,7020,16359,9460,21735,12408,28175,15912,35775,20020,44631,
%U 24780,54839,30240,66495,36448,79695,43452,94535,51300,111111,60040,129519,69720,149855
%N Numerator of n*(n-2)*(2*n-1)/(2*(n-1)).
%H Amiram Eldar, <a href="/A022997/b022997.txt">Table of n, a(n) for n = 2..10000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).
%F G.f.: x^3*(x^6+5x^4+20x^3+75x^2+28x+15)/((x-1)^4*(x+1)^4). - _Ralf Stephan_, Sep 03 2003
%F Sum_{n>=3} 1/a(n) = 11/9 + Pi/6 - 7*log(2)/3. - _Amiram Eldar_, Sep 21 2023
%e Fractions begins with 0, 15/4, 28/3, 135/8, 132/5, 455/12, 360/7, 1071/16, 760/9, 2079/20, 1380/11, 3575/24, ...
%t a[n_] := Numerator[n*(n - 2)*(2*n - 1)/(2*(n - 1))]; Array[a, 50, 2] (* _Amiram Eldar_, Sep 21 2023 *)
%o (PARI) a(n) = numerator(n*(n-2)*(2*n-1)/(2*(n-1))); \\ _Amiram Eldar_, Sep 21 2023
%Y Cf. A022998 (denominators, with an offset shift).
%K nonn,easy,frac
%O 2,2
%A _N. J. A. Sloane_.
%E More terms from _Amiram Eldar_, Sep 21 2023
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