%I #12 Aug 21 2025 03:00:22

%S 0,4,49,225,676,1600,3249,5929,10000,15876,24025,34969,49284,67600,

%T 90601,119025,153664,195364,245025,303601,372100,451584,543169,648025,

%U 767376,902500,1054729,1225449,1416100,1628176,1863225,2122849

%N Squares of second pentagonal numbers: a(n) = (1/4)*n^2*(3*n+1)^2.

%H Leonhard Euler, <a href="http://math.dartmouth.edu/~euler/pages/E542.html">De mirabilibus proprietatibus numerorum pentagonalium</a>, par. 29

%H Leonhard Euler, <a href="https://arxiv.org/abs/math/0505373">On the remarkable properties of the pentagonal numbers</a>, arXiv:math/0505373 [math.HO], 2006.

%F G.f.: x*(4+29*x+20*x^2+x^3)/(1-x)^5. - _Colin Barker_, Feb 14 2012

%Y Equals A005449(n)^2. Cf. A100255.

%K nonn,easy

%O 0,2

%A _Ralf Stephan_, Nov 13 2004