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%I #17 Sep 08 2022 08:45:45
%S 1,45,557,3473,14417,45965,121997,283137,593281,1147213,2079309,
%T 3573329,5873297,9295469,14241389,21212033,30823041,43821037,61101037,
%U 83724945,112941137,150205133,197201357,255865985,328410881,417348621,525518605
%N G.f.: (1+38*x+263*x^2+484*x^3+263*x^4+38*x^5+x^6)/(1-x)^7.
%C Source: the De Loera et al. article and the Haws website listed in A160747.
%H Vincenzo Librandi, <a href="/A160838/b160838.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = 68*n^6/45 +68*n^5/15 +91*n^4/9 +38*n^3/3 +467*n^2/45 +24*n/5 +1. - _R. J. Mathar_, Sep 11 2011
%F a(0)=1, a(1)=45, a(2)=557, a(3)=3473, a(4)=14417, a(5)=45965, a(6)=121997, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+a(n-7). - _Harvey P. Dale_, Sep 17 2011
%t CoefficientList[Series[(1+38x+263x^2+484x^3+263x^4+38x^5+x^6)/(1-x)^7, {x,0,30}], x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,45, 557, 3473,14417,45965,121997}, 30] (* _Harvey P. Dale_, Sep 17 2011 *)
%o (Magma) [68*n^6/45 +68*n^5/15 +91*n^4/9 +38*n^3/3 +467*n^2/45 +24*n/5 +1: n in [0..30]]; // _Vincenzo Librandi_, Sep 19 2011
%o (PARI) x='x+O('x^30); Vec((1+38*x+263*x^2+484*x^3+263*x^4+38*x^5+x^6)/(1-x)^7) \\ _G. C. Greubel_, Apr 28 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 18 2009