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%I #9 Aug 28 2019 16:33:48
%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, A113264-A113269, for m=0.. 10.
%H W. Lang: <a href="/A112707/a112707.txt">First 10 rows.</a>
%F a(n, m)=sum(C(k)*(-m)^k, k=0..n-m), 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)/(1-x), where c(x):=(1-sqrt(1-4*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
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