%I #10 Mar 12 2017 14:09:04
%S 1,10,1,80,20,1,560,260,30,1,3584,2720,540,40,1,21504,24768,7480,920,
%T 50,1,122880,204288,87552,15840,1400,60,1,675840,1562880,908352,
%U 225936,28800,1980,70,1,3604480,11264000,8595200,2813696,483920,47360,2660,80
%N A convolution triangle of numbers obtained from A036070.
%C a(n,m) := s1p(5; 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(5; 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) = 4*(4*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*(1-6*x+16*x^2-16*x^3)/(1-4*x)^4)^m.
%e 1;
%e 10,1;
%e 80,20,1;
%e 560,260,30,1;
%e 3584,2720,540,40,1;
%e ...
%Y a(n, 1)= A036070(n-1). Row sums = A045624(n).
%K easy,nonn,tabl
%O 1,2
%A _Wolfdieter Lang_