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%I #8 Mar 31 2012 13:19:57
%S 1,15,1,175,30,1,1750,575,45,1,15750,8750,1200,60,1,131250,114625,
%T 24375,2050,75,1,1031250,1347500,414750,52000,3125,90,1,7734375,
%U 14575000,6208125,1084875,95000,4425,105,1,55859375,147468750,84184375
%N A convolution triangle of numbers obtained from A036083.
%C a(n,m) := s1p(6; 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(6; 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) = 5*(5*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*(1-10*x+50*x^2-125*x^3+125*x^4)/(1-5*x)^5)^m.
%e {1}; {15,1}; {175,30,1}; {1750,575,45,1}; {15750,8750,1200,60,1}; ...
%Y a(n, 1)= A036083(n-1). Row sums = A046088(n).
%K easy,nonn,tabl
%O 1,2
%A _Wolfdieter Lang_
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