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%I #23 Sep 08 2022 08:45:45
%S 1,154,2287,14725,61147,193546,509293,1172305,2438317,4684258,8441731,
%T 14434597,23620663,37237474,56852209,84415681,122320441,173462986,
%U 241310071,329969125,444262771,589807450,773096149,1001585233
%N Expansion of (1+147*x+1230*x^2+1915*x^3+744*x^4+66*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="/A160841/b160841.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+3*n*(n+1)*(38*n^4+112*n^3+183*n^2+127*n+50)/20. - _R. J. Mathar_, Sep 17 2011
%F a(0)=1, a(1)=154, a(2)=2287, a(3)=14725, a(4)=61147, a(5)=193546, a(6)=509293, 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_, Feb 11 2015
%p seq(coeff(series((1+147*x+1230*x^2+1915*x^3+744*x^4+66*x^5+x^6)/(1-x)^7, x,n+1),x,n),n=0..25); # _Muniru A Asiru_, Apr 29 2018
%t CoefficientList[Series[(1+147x+1230x^2+1915x^3+744x^4+66x^5+x^6)/(1-x)^7, {x,0,30}], x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1, 154, 2287,14725,61147,193546,509293},30] (* _Harvey P. Dale_, Feb 11 2015 *)
%o (Magma) [1+3*n*(n+1)*(38*n^4+112*n^3+183*n^2+127*n+50)/20: n in [0..30]]; // _Vincenzo Librandi_, Sep 19 2011
%o (PARI) x='x+O('x^30); Vec((1+147*x+1230*x^2+1915*x^3+744*x^4+66*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
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