%I #27 Mar 07 2022 03:07:37
%S 196,900,19600,41616,256036,422500,1537600,2238016,6100900,8236900,
%T 18696976,24010000,48024900,59505796,108493056,130873600,222308100,
%U 262634436,421891600,490179600,752624356,862596900,1275918400,1445824576,2072616676,2326132900,3246720400
%N Squares of even square pyramidal numbers.
%H Vincenzo Librandi, <a href="/A014798/b014798.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
%F G.f.: -4*(49*x^10 +176*x^9 +4381*x^8 +4448*x^7 +26290*x^6 +11232*x^5 +26290*x^4 +4448*x^3 +4381*x^2 +176*x +49)/((x -1)^7*(x +1)^6). - _Colin Barker_, Nov 16 2012
%F a(n) = A015222(n+1)^2. - _R. J. Mathar_, Jul 30 2016
%F Sum_{n>=0} 1/a(n) = (165/4 + 18*sqrt(2))*Pi^2 + 54*Pi - 828. - _Amiram Eldar_, Mar 07 2022
%t CoefficientList[Series[- 4 (49 x^10 + 176 x^9 + 4381 x^8 + 4448 x^7 + 26290 x^6 + 11232 x^5 + 26290 x^4 + 4448 x^3 + 4381 x^2 + 176 x + 49)/((x - 1)^7 (x + 1)^6), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)
%t Select[Table[n*(n + 1)*(2*n + 1)/6, {n, 1, 70}], EvenQ]^2 (* _Amiram Eldar_, Mar 07 2022 *)
%Y Cf. A014797, A015222.
%K nonn,easy
%O 0,1
%A _Mohammad K. Azarian_