A099196 - OEIS

%I #32 Jun 09 2023 11:22:28

%S 0,1,18,163,996,4645,17718,57799,166344,432073,1030490,2286955,

%T 4772780,9446125,17852030,32398735,56730512,96220561,158611106,

%U 254831667,400030580,614859189,927052742,1373356887,2001853784,2874747225,4071671786,5693596923,7867403068,10751213181

%N a(n) = n*(2*n^8 + 84*n^6 + 798*n^4 + 1636*n^2 + 315)/2835.

%H Seiichi Manyama, <a href="/A099196/b099196.txt">Table of n, a(n) for n = 0..10000</a>

%H 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 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F a(n) = n*(2*n^8 + 84*n^6 + 798*n^4 + 1636*n^2 + 315)/2835.

%F G.f.: x*(1+x)^8/(1-x)^10. [_Colin Barker_, May 01 2012]

%F a(n) = 18*a(n-1)/(n-1) + a(n-2) for n > 1. - _Seiichi Manyama_, Jun 06 2018

%o (PARI) concat(0, Vec(x*(1+x)^8/(1-x)^10 + O(x^40))) \\ _Michel Marcus_, Dec 14 2015

%Y Similar sequences: A005900 (m=3), A014820(n-1) (m=4), A069038 (m=5), A069039 (m=6), A099193 (m=7), A099195 (m=8), A099197 (m=10).

%Y Cf. A000332.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Nov 16 2004

%E More terms from _Michel Marcus_, Dec 14 2015