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%I #9 Aug 29 2019 16:30:50
%S 1,21,1,336,42,1,4536,1113,63,1,54432,23184,2331,84,1,598752,412272,
%T 65205,3990,105,1,6158592,6531840,1518048,139860,6090,126,1,60046272,
%U 94618368,30912840,4010769,256410,8631,147,1,560431872,1274921856
%N A convolution triangle of numbers obtained from A036224.
%C Signed version: (-1)^(n-m)*a(n, m) := s1(7; n,m).
%C a(n,m) := s1p(7; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle), A030523=s1p(3), A036068=s1p(4), A030526=s1p(5) and A030527=s1p(6).
%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.
%H W. Lang, <a href="/A132166/a132166.txt">First ten rows</a>.
%F a(n, m) = 6*(6*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.
%F G.f. for m-th column: ((1-(1-6*x)^6)/(36*(1-6*x)^6))^m.
%e {1};{21,1};{336,42,1};{4536,1113,63,1};...; Row polynomial s(3,x)=336*x+42*x^2+x^3.
%Y Related triangle A134141 (S1p(7)).
%Y Cf. A036224(n-1), n>=1 (first column). A132167 (row sums). A132168 (alternating row sums).
%K nonn,easy,tabl
%O 1,2
%A _Wolfdieter Lang_, Oct 12 2007