A160836 - OEIS

%I #13 Sep 08 2022 08:45:45

%S 1,69,1027,6825,29073,93789,250363,582737,1222801,2366005,4289187,

%T 7370617,12112257,19164237,29351547,43702945,63482081,90220837,

%U 125754883,172261449,232299313,308851005,405367227,525813489,674718961

%N G.f.: (1+62*x+565*x^2+1050*x^3+485*x^4+52*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="/A160836/b160836.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) = 1 +n*(n+1)*(277*n^4+629*n^3+1031*n^2+679*n+444)/90. - _R. J. Mathar_, Sep 17 2011

%F a(0)=1, a(1)=69, a(2)=1027, a(3)=6825, a(4)=29073, a(5)=93789, a(6)=250363, 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 01 2015

%t CoefficientList[Series[(1+62x+565x^2+1050x^3+485x^4+52x^5+x^6)/(1-x)^7, {x,0,30}],x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,69,1027,6825,29073,93789,250363},30] (* _Harvey P. Dale_, Sep 01 2015 *)

%o (Magma) [1 +n*(n+1)*(277*n^4+629*n^3+1031*n^2+679*n+444)/90: n in [0..30]]; // _Vincenzo Librandi_, Sep 18 2011

%o (PARI) x='x+O('x^30); Vec((1+62*x+565*x^2+1050*x^3+485*x^4+52*x^5 + x^6)/(1-x)^7) \\ _G. C. Greubel_, Apr 28 2018

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Nov 18 2009