Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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