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 A099193 #40 Sep 17 2023 09:43:34
%S A099193 0,1,14,99,476,1765,5418,14407,34232,74313,149830,284075,511380,
%T A099193 880685,1459810,2340495,3644272,5529233,8197758,11905267,16970060,
%U A099193 23784309,32826266,44673751,60018984,79684825,104642486,136030779,175176964,223619261,283131090,355747103
%N A099193 a(n) = n*(4*n^6 + 70*n^4 + 196*n^2 + 45)/315.
%C A099193 Kim asserts that every nonnegative integer can be represented by the sum of no more than 21 of these numbers.
%C A099193 Starting with 1 = binomial transform of [1, 13, 72, 220, 400, 432, 256, 0, 0, 0, ...], where (1, 13, 72, 220, 400, 432, 256) = row 7 of the Chebyshev triangle A081277. Also = row 7 of the array in A142978. - _Gary W. Adamson_, Jul 19 2008
%H A099193 Seiichi Manyama, <a href="/A099193/b099193.txt">Table of n, a(n) for n = 0..10000</a>
%H A099193 Milan Janjić, <a href="https://arxiv.org/abs/1905.04465">On Restricted Ternary Words and Insets</a>, arXiv:1905.04465 [math.CO], 2019.
%H A099193 Hyun Kwang Kim, <a href="http://dx.doi.org/10.1090/S0002-9939-02-06710-2">On Regular Polytope Numbers</a>, Proc. Amer. Math. Soc., 131 (2003), 65-75.
%H A099193 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).
%F A099193 a(n) = n*(4*n^6 + 70*n^4 + 196*n^2 + 45)/315.
%F A099193 G.f.: x*(1+x)^6/(1-x)^8. - _R. J. Mathar_, Jul 18 2009
%F A099193 a(n) = 14*a(n-1)/(n-1) + a(n-2) for n > 1. - _Seiichi Manyama_, Jun 06 2018
%t A099193 Table[SeriesCoefficient[x (1 + x)^6/(1 - x)^8, {x, 0, n}], {n, 0, 31}] (* _Michael De Vlieger_, Dec 14 2015 *)
%o A099193 (PARI) concat(0, Vec(x*(1+x)^6/(1-x)^8 + O(x^40))) \\ _Michel Marcus_, Dec 14 2015
%Y A099193 Similar sequences: A005900 (m=3), A014820(n-1) (m=4), A069038 (m=5), A069039 (m=6), A099195 (m=8), A099196 (m=9), A099197 (m=10).
%Y A099193 Cf. A000332.
%Y A099193 Cf. A142978, A081277.
%K A099193 easy,nonn
%O A099193 0,3
%A A099193 _Jonathan Vos Post_, Nov 16 2004
%E A099193 More terms from _Michel Marcus_, Dec 14 2015