cp's OEIS Frontend

A086026 a(n) = Sum_{i=1..n} C(i+4,5)^3.

%I A086026 #29 Jan 14 2025 10:38:43
%S A086026 1,217,9478,185094,2185470,18188478,116799606,613592694,2745339597,
%T A086026 10769363605,37850444632,121189368664,358136205336,987118431768,
%U A086026 2559344776920,6286103520984,14712254089533,32974344717237,71073599975686,147860902015750,297836101312750
%N A086026 a(n) = Sum_{i=1..n} C(i+4,5)^3.
%H A086026 G. C. Greubel, <a href="/A086026/b086026.txt">Table of n, a(n) for n = 1..5000</a>
%H A086026 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 A086026 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376, 19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F A086026 a(n) = C(n+5,6)^2*(1 + 279*C(n,1) + 681*C(n,2) + 504*C(n,3) + 126*C(n,4) )/280. - _Yahia Kahloune_, Dec 22 2013
%F A086026 -(n-1)^3*a(n) +(2*n+3)*(n^2+3*n+21)*a(n-1) -(n+4)^3*a(n-2)=0. - _R. J. Mathar_, Dec 22 2013
%F A086026 G.f.: -x*(x^10 +200*x^9 +5925*x^8 +52800*x^7 +182700*x^6 +273504*x^5 +182700*x^4 +52800*x^3 +5925*x^2 +200*x +1) / (x -1)^17. - _Colin Barker_, May 02 2014
%F A086026 a(n) = (n^2/580608000)*(57600 + 4583040*n + 28668304*n^2 + 80791200*n^3 + 133134680*n^4 + 142979760*n^5 + 105929613*n^6 + 55881000*n^7 + 21323540* n^8 + 5904360*n^9 + 1175062*n^10 + 163800*n^11 + 15180*n^12 + 840*n^13 + 21*n^14). - _G. C. Greubel_, Nov 22 2017
%e A086026 a(3) = C(8,6)^2*(1 + 279*C(3,1) + 681*C(3,2) + 504*C(3,3))/280 = 9478. - _Yahia Kahloune_, Dec 22 2013
%p A086026 A086026 := proc(n)
%p A086026     add( binomial(i+4,5)^3,i=1..n) ;
%p A086026 end proc:
%p A086026 seq(A086026(n),n=1..30) ; # _R. J. Mathar_, Dec 22 2013
%t A086026 Table[Sum[Binomial[i + 4, 5]^3, {i, n}], {n, 30}] (* _Wesley Ivan Hurt_, Dec 22 2013 *)
%o A086026 (PARI) a(n) = sum(i=1, n, binomial(i+4, 5)^3); \\ _Michel Marcus_, Dec 22 2013
%o A086026 (Magma) [(n^2/580608000)*(57600 + 4583040*n + 28668304*n^2 + 80791200*n^3 + 133134680*n^4 + 142979760*n^5 + 105929613*n^6 + 55881000*n^7 + 21323540* n^8 + 5904360*n^9 + 1175062*n^10 + 163800*n^11 + 15180*n^12 + 840*n^13 + 21*n^14): n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%Y A086026 Cf. A087127, A024166, A085438 - A085442, A086020 - A086030.
%K A086026 easy,nonn
%O A086026 1,2
%A A086026 _André F. Labossière_, Jul 11 2003
%E A086026 More terms from _Michel Marcus_, Dec 22 2013