A234253 - OEIS

%I #40 Feb 25 2025 09:30:44

%S 1,82,2107,29332,274357,1930726,10948735,52357960,217994860,808970960,

%T 2723733524,8436372248,24304813148,65712993248,167965846148,

%U 408373664744,949291256585,2119095737210,4559798912835,9488531918460,19148848609485,37571357310510

%N a(n) = Sum_{i=1..n} C(7+i,8)^2.

%H Vincenzo Librandi, <a href="/A234253/b234253.txt">Table of n, a(n) for n = 1..1000</a>

%H Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 13.

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).

%F G.f.: x*(x^8 +64*x^7 +784*x^6 +3136*x^5 +4900*x^4 +3136*x^3 +784*x^2 +64*x +1) / (x-1)^18. - _Colin Barker_, May 02 2014

%p A234253:=n->add(binomial(7+i,8)^2, i=1..n); seq(A234253(n), n=1..30); # _Wesley Ivan Hurt_, Dec 23 2013

%t Table[Sum[Binomial[7 + i, 8]^2, {i, n}], {n, 30}] (* _Wesley Ivan Hurt_, Dec 23 2013 *)

%t CoefficientList[Series[(x^8 + 64 x^7 + 784 x^6 + 3136 x^5 + 4900 x^4 + 3136 x^3 + 784 x^2 + 64 x + 1)/(x - 1)^18, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 06 2014 *)

%o (PARI) Vec(x*(x^8 +64*x^7 +784*x^6 +3136*x^5 +4900*x^4 +3136*x^3 +784*x^2 +64*x +1)/(x-1)^18 + O(x^100)) \\ _Colin Barker_, May 02 2014

%Y Cf. A087127, A086023, A086025, A086027, A086029.

%K nonn,easy

%O 1,2

%A _Yahia Kahloune_, Dec 22 2013

%E One term corrected and more terms from _Colin Barker_, May 02 2014