%I A116405
%S A116405 1,0,1,2,1,1,0,3,1,1,6,4,5,1,1,0,10,5,6,1,1,20,15,21,7,7,1,1,0,35,21,28,
%T A116405 8,8,1,1,70,56,84,36,37,9,9,1,1,0,126,84,120,45,46,10,10,1,1,252,210,
%U A116405 330,165,175,56,56,11,11,1,1
%V A116405 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,
               0,35,-21,28,-8,8,
%W A116405 -1,1,70,-56,84,-36,37,-9,9,-1,1,0,126,-84,120,-45,46,-10,10,-1,1,252,
               -210,330,-165,
%X A116405 175,-56,56,-11,11,-1,1
%N A116405 Triangle whose k-th column has e.g.f. sum{j=0..k, (-1)^j*Bessel_I(k+j,
               2x)}.
%C A116405 Alternating sign version of A116399. Row sums are A116406. Product of 
               A007318 and this triangle is A116407.
%e A116405 Triangle begins
%e A116405 1,
%e A116405 0, 1,
%e A116405 2, -1, 1,
%e A116405 0, 3, -1, 1,
%e A116405 6, -4, 5, -1, 1,
%e A116405 0, 10, -5, 6, -1, 1
%Y A116405 Sequence in context: A098599 A129334 A116399 this_sequence A029352 A055168 
               A085144
%Y A116405 Adjacent sequences: A116402 A116403 A116404 this_sequence A116406 A116407 
               A116408
%K A116405 easy,sign,tabl
%O A116405 0,4
%A A116405 Paul Barry (pbarry(AT)wit.ie), Feb 13 2006