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 A267849 #27 May 04 2017 06:03:16 %S A267849 1,1,3,1,6,12,1,9,36,60,1,12,72,240,360,1,15,120,600,1800,2520,1,18, %T A267849 180,1200,5400,15120,20160,1,21,252,2100,12600,52920,141120,181440,1, %U A267849 24,336,3360,25200,141120,564480,1451520,1814400,1,27,432,5040,45360,317520,1693440,6531840,16329600,19958400 %N A267849 Triangular array: T(n,k) is the 2-row creation rook number to place k rooks on a 3 x n board. %C A267849 T(n,k) is the number of ways to place k rooks in a 3 x n Ferrers board (or diagram) under the Goldman-Haglund i-row creation rook mode for i=2. All row heights are 3. %H A267849 Jay Goldman and James Haglund, <a href="http://dx.doi.org/10.1006/jcta.2000.3113">Generalized rook polynomials</a>, J. Combin. Theory A 91 (2000), 509-530. %F A267849 T(n,k) = T(n-1,k) + (k+2) T(n-1,k-1) subject to T(0,0)=1, T(n,k)=0 for n<k and for k<0. %e A267849 The triangle T(n,k) begins in row n=0 with columns 0<=k<=n: %e A267849 1 %e A267849 1 3 %e A267849 1 6 12 %e A267849 1 9 36 60 %e A267849 1 12 72 240 360 %e A267849 1 15 120 600 1800 2520 %e A267849 1 18 180 1200 5400 15120 20160 %e A267849 1 21 252 2100 12600 52920 141120 181440 %e A267849 1 24 336 3360 25200 141120 564480 1451520 1814400 %e A267849 1 27 432 5040 45360 317520 1693440 6531840 16329600 19958400 %Y A267849 Cf. A013610 (1-rook coefficients on the 3xn board), A121757 (2-rook coeffs. on the 2xn board), A013609 (1-rook coeffs. on the 2xn board), A013611 (1-rook coeffs. on the 4xn board), A008279 (2-rook coeffs. on the 1xn board), A082030 (row sums?), A049598 (column k=2), A007531 (column k=3 w/o factor 10), A001710 (diagonal?). %K A267849 nonn,easy,tabl %O A267849 0,3 %A A267849 _Ken Joffaniel M. Gonzales_, Jan 21 2016 %E A267849 Triangle simplified (reversing rows, offset 0). - _R. J. Mathar_, May 03 2017