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 A302561 #18 May 04 2024 00:31:33
%S A302561 1,121,1068,4720,14705,36981,80416,157368,284265,482185,777436,
%T A302561 1202136,1794793,2600885,3673440,5073616,6871281,9145593,11985580,
%U A302561 15490720,19771521,24950101,31160768,38550600,47280025,57523401,69469596,83322568,99301945
%N A302561 Partial sums of A092182.
%C A302561 Geometrically, the partial sums of A092182 may be interpreted as 5-dimensional hexacosichoronal hyperpyramidal numbers. The hexacosichoron is a convex regular 4-D polytope with Schlaefli symbol {3,3,5}.
%H A302561 Colin Barker, <a href="/A302561/b302561.txt">Table of n, a(n) for n = 1..1000</a>
%H A302561 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A302561 a(n) = Sum_{k=1..n} A092182(k).
%F A302561 From _Colin Barker_, Aug 15 2018: (Start)
%F A302561 G.f.: x*(1 + 115*x + 357*x^2 + 107*x^3) / (1 - x)^6.
%F A302561 a(n) = (n*(12 + n - 64*n^2 + 5*n^3 + 58*n^4)) / 12.
%F A302561 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) for n>6.
%F A302561 (End)
%t A302561 Accumulate[LinearRecurrence[{5,-10,10,-5,1},{1,120,947,3652,9985},30]] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{1,121,1068,4720,14705,36981},30] (* _Harvey P. Dale_, May 04 2024 *)
%o A302561 (PARI) Vec(x*(1 + 115*x + 357*x^2 + 107*x^3) / (1 - x)^6 + O(x^40)) \\ _Colin Barker_, Aug 15 2018
%o A302561 (PARI) a(n) = (n*(12 + n - 64*n^2 + 5*n^3 + 58*n^4)) / 12 \\ _Colin Barker_, Aug 15 2018
%Y A302561 Cf. A092182.
%K A302561 nonn,easy
%O A302561 1,2
%A A302561 _Alejandro J. Becerra Jr._, Aug 15 2018