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%I #2 Mar 30 2012 18:59:14
%S 1,0,1,2,-1,1,0,3,-1,1,6,-4,5,-1,1,0,10,-5,6,-1,1,20,-15,21,-7,7,-1,1,
%T 0,35,-21,28,-8,8,-1,1,70,-56,84,-36,37,-9,9,-1,1,0,126,-84,120,-45,
%U 46,-10,10,-1,1,252,-210,330,-165,175,-56,56,-11,11,-1,1
%N Triangle whose k-th column has e.g.f. sum{j=0..k, (-1)^j*Bessel_I(k+j,2x)}.
%C Alternating sign version of A116399. Row sums are A116406. Product of A007318 and this triangle is A116407.
%e Triangle begins
%e 1,
%e 0, 1,
%e 2, -1, 1,
%e 0, 3, -1, 1,
%e 6, -4, 5, -1, 1,
%e 0, 10, -5, 6, -1, 1
%K easy,sign,tabl
%O 0,4
%A _Paul Barry_, Feb 13 2006
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