%I #8 Feb 12 2013 15:38:58
%S 1,1,2,1,12,6,1,24,18,108,24,1,40,80,360,540,960,120,1,60,150,100,900,
%T 3600,900,4800,10800,9000,720,1,84,252,420,1890,9450,6300,9450,16800,
%U 100800,50400,63000,189000,90720,5040,1,112,392,784,490,3528,21168,35280,26460,35280,47040,352800,235200,705600,88200,294000,2352000,1764000,846720,3175200,987840,40320,1,144,576,1344,2016,6048,42336
%N Irregular triangle T(n,k) = binomial(n-1,m-1)*m!*A036040(n,k), where m=A036043(n,k).
%C This is a refinement of the triangle A048743.
%C Row n has A000041(n) elements.
%C The sequence can be derived by expanding A007318 and A000142 and using A036040.
%C For example, row four can be derived using
%C (1 3 3 3 1) times (1 2 2 6 24) times (1 4 3 6 1) = (1 24 18 108 24)
%e The table begins:
%e 1
%e 1...2
%e 1..12...6
%e 1..24..18..108..24
%Y Cf. A045531 (row sums), A048743, A007318, A036040.
%K nonn,tabf
%O 1,3
%A _Alford Arnold_, Oct 22 2010
%E Row 6 onwards and definition by _R. J. Mathar_, Feb 12 2013