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%I #27 Jun 11 2023 12:19:06
%S 1,257,10257,170257,1670882,11505378,61292514,268652514,1009853139,
%T 3352413139,10042998755,27598188771,70457539396,168802499396,
%U 382616259396,825980472132,1707628231653,3396588391653,6525595601653,12150082161653,21987344308134,38769279231910
%N a(n) = Sum_{i=1..n} C(i+2,3)^4.
%H T. D. Noe, <a href="/A086022/b086022.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).
%F G.f.: x*(1+x)*(x^8 +242*x^7 +6508*x^6 +43174*x^5 +84950*x^4 +43174*x^3 +6508*x^2 +242*x + 1) / (x-1)^14 . - _R. J. Mathar_, Dec 22 2013
%F (n-1)^4*a(n) +(-2*n^4 -4*n^3 -30*n^2 -28*n -17)*a(n-1) +(n+2)^4*a(n-2)=0. - _R. J. Mathar_, Dec 22 2013
%F a(n) = C(n+3,4)*[-41*F3(n) +350*(47*C(n+8,9) + 1749*C(n+7,9) + 9292*C(n+6,9) + 9292*C(n+5,9) + 1749*C(n+4,9) + 47*C(n+3,9))]/15015, where F3(n) = -C(3,0)*C(n+3,0) + C(4,1)*C(n+3,1) - C(5,2)*C(n+3,2) + C(6,3)*C(n+3,3). The value of F3(n), (n=0..8) is: 1, 35, 119, 273, 517, 871, 1355, 1989, 2793, ... - _Yahia Kahloune_, Dec 23 2013
%F a(n) = (n/12972960)*(-8856 + 60060*n^2 + 165165*n^3 + 841841*n^4 + 2462460*n^5 + 3709420*n^6 + 3243240*n^7 + 1756755*n^8 + 600600*n^9 + 126490*n^10 + 15015*n^11 + 770*n^12). - _G. C. Greubel_, Nov 22 2017
%e a(8) = C(11,4)*[-41*2793 + 350*(47*C(16,9) + 1749*C(15,9) + 9292*C(14,9) + 9292*C(13,9) + 1749*C(12,9) + 47*C(11,9))]/15015 = 268652514 .
%t Accumulate[Binomial[Range[3,30],3]^4] (* _Harvey P. Dale_, Oct 09 2016 *)
%o (PARI) for(n=1,30, print1((n/12972960)*(-8856 + 60060*n^2 + 165165*n^3 + 841841*n^4 + 2462460*n^5 + 3709420*n^6 + 3243240*n^7 + 1756755*n^8 + 600600*n^9 + 126490*n^10 + 15015*n^11 + 770*n^12), ", ")) \\ _G. C. Greubel_, Nov 22 2017
%o (Magma) [(n/12972960)*(-8856 +60060*n^2 +165165*n^3 +841841*n^4 +2462460*n^5 +3709420*n^6 +3243240*n^7 +1756755*n^8 +600600*n^9 +126490*n^10 +15015*n^11 +770*n^12): n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%Y Cf. A086020, A086021, A086023, A086024, A086025, A086026, A086027, A086028, A086029, A086030, A087127, A024166, A085438, A085439, A085440, A085441, A085442.
%K easy,nonn
%O 1,2
%A _André F. Labossière_, Jul 11 2003
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