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%I #8 Mar 31 2012 13:19:57
%S 1,6,1,30,12,1,135,96,18,1,567,630,198,24,1,2268,3654,1701,336,30,1,
%T 8748,19440,12501,3564,510,36,1,32805,96957,82296,31644,6435,720,42,1,
%U 120285,459756,498663,247536,66915,10530,966,48,1,433026,2092959
%N A convolution triangle of numbers obtained from A036068.
%C a(n,m) := s1p(4; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle). Signed version: (-1)^(n-m)*a(n,m) := s1(4; n,m).
%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*(1-3*x+3*x^2)/(1-3*x)^3)^m.
%e {1}; {6,1}; {30,12,1}; {135,96,18,1}; {567,630,198,24,1}; ...
%Y Cf. A030523, A043553. a(n, 1)= A036068(n-1). Row sums = A043553(n).
%K easy,nonn,tabl
%O 1,2
%A _Wolfdieter Lang_
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