A049325 - OEIS

%I #8 Mar 31 2012 13:19:59

%S 1,6,1,16,12,1,16,68,18,1,0,224,156,24,1,0,448,840,280,30,1,0,512,

%T 3072,2080,440,36,1,0,256,7872,10896,4160,636,42,1,0,0,14080,42240,

%U 28240,7296,868,48,1,0,0,16896,123904,145376,60720,11704,1136,54,1,0,0,12288

%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) = 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*p(3, x))^m, p(3, x) := 1+6*x+16*x^2+16*x^3 (row polynomial of A033842(3, m)).

%e {1}; {6,1}; {16,12,1}; {16,68,18,1}; {0,224,156,24,1}; ...

%Y a(n, m) := s1(-3, 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, s1(-2, n, m)= A049324(n, m).

%Y Cf. A049349.

%K easy,nonn,tabl

%O 1,2

%A _Wolfdieter Lang_