This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089514 #8 Mar 17 2023 15:45:35
%S A089514 1,210,31356,4150440,521757936,64043874720,7771495098816,
%T A089514 937759335004800,112842062355914496,13559707534436743680,
%U A089514 1628284591773850622976,195461334300256627599360
%N A089514 Fourth column of triangle A089504.
%C A089514 Convolution of A089513 with powers of 120.
%H A089514 Harvey P. Dale, <a href="/A089514/b089514.txt">Table of n, a(n) for n = 0..480</a>
%H A089514 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (210,-12744,241920,-1036800).
%F A089514 G.f.: 1/((1-3*2*1*x)*(1-4*3*2*x)*(1-5*4*3*x)*(1-6*5*4*x)).
%F A089514 a(n) = A089504(n+4, 4), n>=0.
%F A089514 a(n) = (1350*(6*5*4)^n - 950*(5*4*3)^n + 114*(4*3*2)^n - (3*2*1)^n)/513.
%t A089514 CoefficientList[Series[1/((1-6x)(1-24x)(1-60x)(1-120x)),{x,0,20}],x] (* or *) LinearRecurrence[ {210,-12744,241920,-1036800},{1,210,31356,4150440},20] (* _Harvey P. Dale_, Mar 17 2023 *)
%Y A089514 Cf. A089505, A089513.
%K A089514 nonn,easy
%O A089514 0,2
%A A089514 _Wolfdieter Lang_, Dec 01 2003