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 A304993 #23 May 03 2023 16:06:32
%S A304993 0,4,19,52,110,200,329,504,732,1020,1375,1804,2314,2912,3605,4400,
%T A304993 5304,6324,7467,8740,10150,11704,13409,15272,17300,19500,21879,24444,
%U A304993 27202,30160,33325,36704,40304,44132,48195,52500,57054,61864,66937,72280,77900,83804,89999,96492
%N A304993 a(n) = n*(n + 1)*(7*n + 5)/6.
%C A304993 The sequence provides the sums of the triangular numbers from A000217(n) to A000217(2*n).
%H A304993 Colin Barker, <a href="/A304993/b304993.txt">Table of n, a(n) for n = 0..1000</a>
%H A304993 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A304993 O.g.f.: x*(4 + 3*x)/(1 - x)^4.
%F A304993 E.g.f.: x*(24 + 33*x + 7*x^2)*exp(x)/6.
%F A304993 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A304993 a(n) = -A255211(-n-1).
%F A304993 a(n) + a(-n) = A016742(n).
%F A304993 a(n) = Sum_{k = n..2*n} k*(k+1)/2.
%t A304993 Table[n (n + 1) (7 n + 5)/6, {n, 0, 50}]
%t A304993 LinearRecurrence[{4,-6,4,-1},{0,4,19,52},50] (* _Harvey P. Dale_, May 03 2023 *)
%o A304993 (PARI) concat(0, Vec(x*(4 + 3*x)/(1 - x)^4 + O(x^40))) \\ _Colin Barker_, May 25 2018
%Y A304993 Cf. A000217, A255211.
%Y A304993 Partial sums of A022265.
%Y A304993 Cf. A045943: Sum_{k = n..2*n} k.
%Y A304993 Cf. A050409: Sum_{k = n..2*n} k^2.
%Y A304993 Row sums of the triangle in A141433.
%K A304993 nonn,easy
%O A304993 0,2
%A A304993 _Bruno Berselli_, May 23 2018