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%I #8 Mar 31 2012 13:19:59
%S 1,3,1,3,6,1,0,15,9,1,0,18,36,12,1,0,9,81,66,15,1,0,0,108,216,105,18,
%T 1,0,0,81,459,450,153,21,1,0,0,27,648,1305,810,210,24,1,0,0,0,594,
%U 2673,2970,1323,276,27,1,0,0,0,324,3915,7938
%N A convolution triangle of numbers generalizing Pascal's triangle A007318.
%H W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%F a(n, m) = 3*(3*m-n+1)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1. G.f. for m-th column: (x*p(2, x))^m, p(2, x) := 1+3*x+3*x^2 (row polynomial of A033842(2, m)).
%e {1}; {3,1}; {3,6,1}; {0,15,9,1}; {0,18,36,12,1}; ...
%Y a(n, m) := s1(-2, n, m), a member of a sequence of triangles including s1(0, n, m)= A023531(n, m) (unit matrix) and s1(2, n, m)=A007318(n-1, m-1) (Pascal's triangle). s1(-1, n, m)= A030528.
%Y Cf. A049348, A049404.
%K easy,nonn,tabl
%O 1,2
%A _Wolfdieter Lang_
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