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Squares of even pentagonal pyramidal numbers.
5

%I #29 Feb 07 2024 12:33:12

%S 0,36,324,1600,15876,38416,82944,302500,527076,876096,2160900,3240000,

%T 4734976,9474084,13032100,17640000,30980356,40297104,51840000,

%U 83283876,104162436,129231424,194602500,236421376,285474816,409252900,486202500

%N Squares of even pentagonal pyramidal numbers.

%H Vincenzo Librandi, <a href="/A014800/b014800.txt">Table of n, a(n) for n = 0..1500</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalPyramidalNumber.html">Pentagonal Pyramidal Number</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-15,15,0,20,-20,0,-15,15,0,6,-6,0,-1,1).

%F G.f.: -4*x*(x^16 +143*x^15 +481*x^14 +1394*x^13 +9661*x^12 +10814*x^11 +15996*x^10 +45222*x^9 +25248*x^8 +23414*x^7 +33610*x^6 +9218*x^5 +5203*x^4 +3515*x^3 +319*x^2 +72*x +9)/((x -1)^7*(x^2 +x +1)^6). [_Colin Barker_, Nov 16 2012]

%F a(n) = A015224(n)^2. - _R. J. Mathar_, Jul 30 2016

%t Select[CoefficientList[Series[(x(2x+1))/(x-1)^4,{x,0,50}],x],EvenQ]^2 (* _Harvey P. Dale_, Feb 27 2012 *)

%Y Cf. A002411, A015224, A015223, A014799.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_