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 A245301 #27 Sep 08 2022 08:46:08
%S A245301 0,5,22,58,120,215,350,532,768,1065,1430,1870,2392,3003,3710,4520,
%T A245301 5440,6477,7638,8930,10360,11935,13662,15548,17600,19825,22230,24822,
%U A245301 27608,30595,33790,37200,40832,44693,48790,53130,57720,62567,67678,73060,78720,84665
%N A245301 a(n) = n*(7*n^2 + 15*n + 8)/6.
%C A245301 Row sums of the triangle in A245300.
%H A245301 G. C. Greubel, <a href="/A245301/b245301.txt">Table of n, a(n) for n = 0..1000</a>
%H A245301 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A245301 a(n) = n*(n+1)*(7*n+8)/6 = A002378(n)*A016993(n+1)/6.
%F A245301 a(n) = Sum_{j=0..n} A000217(2n-j)+j. - _Manfred Arens_, Dec 26 2015
%F A245301 G.f.: x*(5 + 2*x)/(1-x)^4. - _Vincenzo Librandi_, Feb 01 2016
%F A245301 E.g.f.: x*(30 + 36*x + 7*x^2)*exp(x)/6. - _G. C. Greubel_, Mar 31 2021
%p A245301 A245301:= n-> n*(n+1)*(7*n+8)/6; seq(A245301(n), n=0..50); # _G. C. Greubel_, Mar 31 2021
%t A245301 Table[n (7 n^2 + 15 n + 8)/6, {n, 0, 50}] (* _Vincenzo Librandi_, Feb 01 2016 *)
%t A245301 LinearRecurrence[{4,-6,4,-1},{0,5,22,58},50] (* _Harvey P. Dale_, Sep 21 2019 *)
%o A245301 (Haskell)
%o A245301 a245301 n = n * (n * (7 * n + 15) + 8) `div` 6
%o A245301 (PARI) a(n)=n*(7*n^2+15*n+8)/6 \\ _Charles R Greathouse IV_, Feb 01 2016
%o A245301 (Magma) [n*(7*n^2+15*n+8)/6: n in [0..60]]; // _Vincenzo Librandi_, Feb 01 2016
%o A245301 (Sage) [n*(n+1)*(7*n+8)/6 for n in (0..50)] # _G. C. Greubel_, Mar 31 2021
%Y A245301 Cf. A002378, A016993, A245300, A254407.
%K A245301 nonn,easy
%O A245301 0,2
%A A245301 _Reinhard Zumkeller_, Jul 17 2014