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%I #19 Sep 08 2022 08:45:45
%S 1,69,1029,6857,29273,94589,252813,589009,1236913,2394805,4343637,
%T 7467417,12275849,19429229,29765597,44330145,64406881,91552549,
%U 127632805,174860649,235837113,313594205,411640109,534006641,685298961
%N Expansion of: (1+62*x+567*x^2+1068*x^3+503*x^4+54*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="/A160834/b160834.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 G.f.: (1+62*x+567*x^2+1068*x^3+503*x^4+54*x^5+x^6)/(1-x)^7.
%F a(n) = 1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15. - _R. J. Mathar_, Sep 17 2011
%F 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). - _Wesley Ivan Hurt_, Oct 01 2021
%p A160834:=n->1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15: seq(A160834(n), n=0..30); # _Wesley Ivan Hurt_, Mar 04 2014
%t Table[1 + n*(n + 1)*(47*n^4 + 104*n^3 + 171*n^2 + 114*n + 74)/15, {n, 0, 30}] (* _Wesley Ivan Hurt_, Mar 04 2014 *)
%o (Magma) [1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n+74)/15: n in [0..30]]; // _Vincenzo Librandi_, Sep 18 2011
%o (PARI) for(n=0, 30, print1(1+n*(n+1)*(47*n^4+104*n^3+171*n^2+114*n +74)/15, ", ")) \\ _G. C. Greubel_, Apr 28 2018
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Nov 18 2009
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