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A099197 a(n) = (n^2)*(2*n^8+120*n^6+1806*n^4+7180*n^2+5067)/14175.

%I A099197 #44 Jan 29 2025 07:53:32
%S A099197 0,1,20,201,1360,7001,29364,104881,329024,927441,2390004,5707449,
%T A099197 12767184,26986089,54284244,104535009,193664256,346615329,601446996,
%U A099197 1014889769,1669752016,2684641785,4226553716,6526963345,9902174016,14778775025,21725194036,31490462745
%N A099197 a(n) = (n^2)*(2*n^8+120*n^6+1806*n^4+7180*n^2+5067)/14175.
%H A099197 Seiichi Manyama, <a href="/A099197/b099197.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from T. D. Noe)
%H A099197 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 A099197 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A099197 a(n) = (n^2)*(2*n^8+120*n^6+1806*n^4+7180*n^2+5067)/14175.
%t A099197 A099197[n_] := n^2*(2*n^2*(n^6 + 60*n^4 + 903*n^2 + 3590) + 5067)/14175;
%t A099197 Array[A099197, 30, 0] (* _Paolo Xausa_, Jan 29 2025 *)
%o A099197 (PARI) a(n)=n^2*(2*n^8+120*n^6+1806*n^4+7180*n^2+5067)/14175 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A099197 Similar sequences: A005900 (m=3), A014820(n-1) (m=4), A069038 (m=5), A069039 (m=6), A099193 (m=7), A099195 (m=8), A099196 (m=9).
%Y A099197 Cf. A000332.
%K A099197 easy,nonn
%O A099197 0,3
%A A099197 _Jonathan Vos Post_, Nov 16 2004