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 A089517 #10 Aug 29 2019 16:02:13
%S A089517 1,18,9,432,1,672,14400,243,47520,648000,27,36396,3790800,38102400,1,
%T A089517 9765,5115888,354715200,2844979200,1107,2499552,757646784,39182330880,
%U A089517 263363788800,54,546453,592216272,123294623040,5089348454400
%N A089517 Array used for numerators of g.f.s for column sequences of array A078741 ((3,3)-Stirling2).
%C A089517 The row length sequence for this array is A004396(n-2)=floor((2*n-3)/3), n>=3: [1,1,2,3,3,4,5,5,6,7,7,8,9,9,10,...].
%C A089517 The g.f. G(m,x) for the m-th column sequence (with leading zeros) of array A078741 is given there. The recurrence is G(m,x) = x*(3*fallfac(m-1,2)*G(m-1,x) + 3*(m-2)*G(m-2,x) + G(m-3,x))/(1-fallfac(m,3)*x), m>=4, with inputs G(1,x)=0=G(2,x) and G(3,x)=x/(1-(3*2*1)*x); where fallfac(n,m) := A008279(n,m) (falling factorials). Computed from the Blasiak et al. reference, eqs. (20) and (21) with r=3: recurrence for S_{3,3}(n,k).
%H A089517 W. Lang, <a href="/A089517/a089517.txt">First 11 rows</a>.
%F A089517 a(n, m) from: sum(a(n, m)*x^m, m=0..kmax(n)) = G(n, x)* product(1-fallfac(p, 3)*x, p=3..n)/x^ceiling(n/3), n>=3, with G(n, x) defined from the recurrence given above and kmax(n) := A004523(n-3)= floor(2*(n-3)/3) = A004396(n-3)-1.
%e A089517 [1]; [18]; [9,423]; [1,672,14400]; [243,47520,648000]; ...
%e A089517 G(4,x)/(x^2) = 18/((1-3*2*1*x)*(1-4*3*2*x)). kmax(4)=0, hence P(4,x)=a(4,0)=18; x^2 from x^ceiling(4/3).
%K A089517 nonn,easy,tabf
%O A089517 3,2
%A A089517 _Wolfdieter Lang_, Dec 01 2003