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 A082047 #15 Jan 25 2024 15:22:02
%S A082047 1,2,7,24,69,170,371,736,1353,2338,3839,6040,9165,13482,19307,27008,
%T A082047 37009,49794,65911,85976,110677,140778,177123,220640,272345,333346,
%U A082047 404847,488152,584669,695914,823515,969216,1134881,1322498,1534183
%N A082047 Diagonal sums of number array A082046.
%H A082047 G. C. Greubel, <a href="/A082047/b082047.txt">Table of n, a(n) for n = 0..1000</a>
%H A082047 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A082047 a(n) = (n^5+15*n^3+14*n+30)/30 = (n+1)*(n^4-n^3+16*n^2-16*n+30)/30.
%F A082047 From _G. C. Greubel_, Dec 24 2022: (Start)
%F A082047 G.f.: (1 - 4*x + 10*x^2 - 8*x^3 + 5*x^4)/(1-x)^6.
%F A082047 E.g.f.: (1/30)*(30 +30*x +60*x^2 +40*x^3 +10*x^4 +x^5)*exp(x). (End)
%t A082047 Table[(n+1)*(n*(n-1)*(n^2+16)+30)/30, {n,0,40}] (* _G. C. Greubel_, Dec 24 2022 *)
%t A082047 LinearRecurrence[{6,-15,20,-15,6,-1},{1,2,7,24,69,170},40] (* _Harvey P. Dale_, Jan 25 2024 *)
%o A082047 (PARI) a(n) = (n^5+15*n^3+14*n+30)/30; \\ _Michel Marcus_, Jan 22 2016
%o A082047 (Magma) [(n+1)*(n*(n-1)*(n^2+16)+30)/30: n in [0..40]]; // _G. C. Greubel_, Dec 24 2022
%o A082047 (SageMath) [(n+1)*(n*(n-1)*(n^2+16)+30)/30 for n in range(41)] # _G. C. Greubel_, Dec 24 2022
%Y A082047 Cf. A082045, A082046, A082107.
%K A082047 easy,nonn
%O A082047 0,2
%A A082047 _Paul Barry_, Apr 03 2003