|
%I #8 Mar 31 2012 13:19:59
%S 1,15,1,120,30,1,540,465,45,1,1296,4680,1035,60,1,1296,33192,15795,
%T 1830,75,1,0,171072,176688,37260,2850,90,1,0,641520,1521828,563409,
%U 72450,4095,105,1,0,1710720,10359360,6686064,1375605,124740,5565,120,1
%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) = 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. G.f. for m-th column: (x*p(5, x))^m, p(5, x) := 1+15*x+120*x^2+540*x^3+1296*x^4+1296*x^5 (row polynomial of A033842(5, m)).
%e {1}; {15,1}; {120,30,1}; {540,465,45,1}; {1296,4680,1035,60,1}; ...
%Y a(n, m) := s1(-5, 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. A049351.
%K easy,nonn,tabl
%O 1,2
%A _Wolfdieter Lang_
|
