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A099195 a(n) = (n^2)*( n^6 + 28*n^4 + 154*n^2 + 132 )/315.

%I A099195 #32 Jun 09 2023 08:53:30
%S A099195 0,1,16,129,704,2945,10128,29953,78592,187137,411280,845185,1640640,
%T A099195 3032705,5373200,9173505,15158272,24331777,38058768,58161793,87037120,
%U A099195 127791489,184402064,261902081,366594816,506298625,690625936,931299201,1242506944,1641303169,2148053520
%N A099195 a(n) = (n^2)*( n^6 + 28*n^4 + 154*n^2 + 132 )/315.
%D A099195 H. S. M. Coxeter, Regular Polytopes, New York: Dover, 1973.
%H A099195 Seiichi Manyama, <a href="/A099195/b099195.txt">Table of n, a(n) for n = 0..10000</a>
%H A099195 Milan Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550 [math.CO], 2013.
%H A099195 Milan Janjic and B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014) # 14.3.5
%H A099195 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 A099195 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A099195 a(n) = (n^2)*( n^6 + 28*n^4 + 154*n^2 + 132 )/315.
%F A099195 G.f.: x*(1+x)^7/(1-x)^9. [_R. J. Mathar_, Jul 18 2009]
%F A099195 a(n) = 16*a(n-1)/(n-1) + a(n-2) for n > 1. - _Seiichi Manyama_, Jun 06 2018
%t A099195 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,1,16,129,704,2945,10128,29953,78592},40] (* _Harvey P. Dale_, Jan 23 2019 *)
%o A099195 (PARI) concat(0, Vec(x*(1+x)^7/(1-x)^9 + O(x^40))) \\ _Michel Marcus_, Dec 14 2015
%Y A099195 Similar sequences: A005900 (m=3), A014820(n-1) (m=4), A069038 (m=5), A069039 (m=6), A099193 (m=7), A099196 (m=9), A099197 (m=10).
%Y A099195 Cf. A000332.
%K A099195 easy,nonn
%O A099195 0,3
%A A099195 _Jonathan Vos Post_, Nov 16 2004