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%I #11 Jun 13 2015 00:54:18
%S 0,9,89,439,1519,4214,10038,21378,41778,76263,131703,217217,344617,
%T 528892,788732,1147092,1631796,2276181,3119781,4209051,5598131,
%U 7349650,9535570,12238070,15550470,19578195,24439779,30267909,37210509,45431864,55113784
%N n*(n+1)*(n+2)*(n+3)*(20*n^2+72*n+43)/360.
%C Second but last (highest) coefficient of the Meixner polynomial M_n(x); 5th column of A060338.
%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. -x*(9+26*x+5*x^2) / (x-1)^7 .
%p A214616 := proc(n)
%p n*(n+1)*(n+2)*(n+3)*(20*n^2+72*n+43)/360 ;
%p end proc:
%t Table[Times@@(n+Range[0,3])(20n^2+72n+43)/360,{n,0,30}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{0,9,89,439,1519,4214,10038},40] (* _Harvey P. Dale_, Dec 24 2014 *)
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Mar 06 2013