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 A257199 #35 Feb 08 2022 22:13:46
%S A257199 1,5,16,41,91,182,336,582,957,1507,2288,3367,4823,6748,9248,12444,
%T A257199 16473,21489,27664,35189,44275,55154,68080,83330,101205,122031,146160,
%U A257199 173971,205871,242296,283712,330616,383537,443037,509712,584193,667147,759278,861328,974078
%N A257199 a(n) = n*(n+1)*(n+2)*(n^2+2*n+17)/120.
%C A257199 Antidiagonal sums of the array of pyramidal numbers shown in Table 2 of Sardelis and Valahas paper (see A261720).
%C A257199 This is the case j = 3 of (n^2 + (j-1)*n + (j+1)^2 + 1)*binomial(n+j-1, j)/((j+1)*(j+2)), where j is the space dimension: a(n) = (n^2+2*n+17)*binomial(n+2,3)/20.
%C A257199 The sequence is the binomial transform of (1, 4, 7, 7, 4, 1, 0, 0, 0, ...). - _Gary W. Adamson_, Aug 26 2015
%H A257199 D. A. Sardelis and T. M. Valahas, <a href="http://arxiv.org/abs/0805.4070">On Multidimensional Pythagorean Numbers</a>, arXiv:0805.4070 [math.GM], 2008.
%H A257199 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A257199 G.f.: x*(1 - x + x^2)/(1 - x)^6.
%t A257199 Table[n (n + 1) (n + 2) (n^2 + 2n + 17)/120, {n, 40}]
%t A257199 LinearRecurrence[{6,-15,20,-15,6,-1},{1,5,16,41,91,182},40] (* _Harvey P. Dale_, Mar 18 2018 *)
%o A257199 (Magma) [n*(n+1)*(n+2)*(n^2+2*n+17)/120: n in [1..40]]; // _Vincenzo Librandi_, Apr 18 2015
%Y A257199 Cf. A257200, A257201.
%Y A257199 For another version of the array, see A080851.
%K A257199 nonn,easy
%O A257199 1,2
%A A257199 _Luciano Ancora_, Apr 18 2015