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%I #20 Aug 19 2023 10:33:34
%S 4,27,104,305,756,1667,3368,6354,11340,19327,31680,50219,77324,116055,
%T 170288,244868,345780,480339,657400,887589,1183556,1560251,2035224,
%U 2628950,3365180,4271319,5378832
%N Eighth column (k=7) of sextinomial array A063260.
%H Ray Chandler, <a href="/A063262/b063262.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).
%F a(n) = A063260(n+2, 7 )= (n+1)*(n+2)*(n^5+32*n^4+413*n^3+2722*n^2+9432*n+10080)/7!.
%F G.f.: (4-5*x+5*x^3-4*x^4+x^5)/(1-x)^8; the numerator polynomial is N6(7, x) from row n=7 of array A063261.
%F a(n) = 4*C(n+2,2) + 15*C(n+2,3) + 20*C(n+2,4) + 15*C(n+2,5) + 6*C(n+2,6) + C(n+2,7) (see comment in A213888). - _Vladimir Shevelev_ and _Peter J. C. Moses_, Jun 22 2012
%t CoefficientList[Series[(4-5x+5x^3-4x^4+x^5)/(1-x)^8,{x,0,30}],x] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{4,27,104,305,756,1667,3368,6354},30] (* _Harvey P. Dale_, Mar 07 2023 *)
%Y Cf. A062989, A063260, A063261, A063263, A063264, A213888.
%K nonn,easy
%O 0,1
%A _Wolfdieter Lang_, Jul 24 2001
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