%I
%S 1,1,1,1,0,1,1,2,1,1,1,3,7,2,1,1,11,33,16,3,1,1,31,191,119,29,
%T 4,1,1,101,1153,1015,291,46,5,1,1,328,7295,9191,3293,579,67,6,
%U 1,1,1102,47617,87037,39715,8171,1013,92,7,1,1,3760,318463,851186,500957,123079,17131,1623,121
%N Triangle built from partial sums of Catalan numbers multiplied by powers of nonpositive numbers.
%C The column sequences (without leading zeros) begin with A000012 (powers of 1), A032357(n)*(1)^n, A064306(n)*(1)^n, A112710, A112711, A113264A113269, for m=0.. 10.
%H W. Lang: <a href="http://wwwitp.physik.unikarlsruhe.de/~wl/EISpub/A112707.text">First 10 rows.</a>
%F a(n, m)=sum(C(k)*(m)^k, k=0..nm), with C(k):=A000108(k) (Catalan) if n>m>0; a(n, n)=1, a(n, 0)=1, n>=0; a(n, m)=0 if n<m.
%F G.f. for column m>=0 (without leading zeros): c(m*x)/(1x), where c(x):=(1sqrt(14*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
%Y Row sums give A112708. Unsigned row sums give A112709.
%Y Cf. A112705 (similar triangle with powers of positive numbers).
%K sign,easy,tabl
%O 0,8
%A _Wolfdieter Lang_, Oct 31 2005
