This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081282 #20 Sep 08 2022 08:45:09
%S A081282 0,1,6,22,62,147,308,588,1044,1749,2794,4290,6370,9191,12936,17816,
%T A081282 24072,31977,41838,53998,68838,86779,108284,133860,164060,199485,
%U A081282 240786,288666,343882,407247,479632,561968,655248,760529,878934,1011654
%N A081282 Generalized centered polygonal numbers.
%C A081282 Partial sums of A006007.
%H A081282 Vincenzo Librandi, <a href="/A081282/b081282.txt">Table of n, a(n) for n = 0..1000</a>
%H A081282 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A081282 a(n) = 2*C(n+3, 5) + C(n+2, 3).
%F A081282 G.f.: x*(1+x^2)/(1-x)^6.
%F A081282 a(n) = n*(n+1)*(n+2)*(n^2+2*n+7)/60. - _Carl Najafi_, Nov 18 2012
%F A081282 a(0)=0, a(1)=1, a(2)=6, a(3)=22, a(4)=62, a(5)=147, a(n)=6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - _Harvey P. Dale_, Jan 09 2014
%t A081282 CoefficientList[Series[x (1 + x^2) / (1 - x)^6, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%t A081282 LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,6,22,62,147},40] (* _Harvey P. Dale_, Jan 09 2014 *)
%o A081282 (Magma) [(n*(n+1)*(n+2)*(n^2+2*n+7))/60: n in [0..35]]; // _Vincenzo Librandi_, Aug 07 2013
%Y A081282 Cf. A081284.
%K A081282 nonn,easy
%O A081282 0,3
%A A081282 _Paul Barry_, Mar 17 2003