%I A085737
%S A085737 1,1,1,1,1,1,0,1,1,0,1,1,2,1,1,0,1,1,1,1,0,1,1,1,8,1,1,1,0,
%T A085737 1,1,4,4,1,1,0,1,1,1,4,8,4,1,1,1,0,1,1,8,4,4,8,1,1,0,5,
%U A085737 5,7,4,116,32,116,4,7,5,5,0,5,5,32,28,16,16,28,32,5,5,0
%V A085737 1,1,1,1,1,1,0,1,1,0,-1,1,2,1,-1,0,-1,1,1,-1,0,1,-1,-1,8,-1,-1,1,0,
%W A085737 1,-1,4,4,-1,1,0,-1,1,-1,-4,8,-4,-1,1,-1,0,-1,1,-8,4,4,-8,1,-1,0,5,
%X A085737 -5,7,4,-116,32,-116,4,7,-5,5,0,5,-5,32,-28,16,16,-28,32,-5,5,0
%N A085737 Numerators in triangle formed from Bernoulli numbers.
%C A085737 Triangle is determined by rules 0) the top number is 1; 1) each number 
               is the sum of the two below it; 2) it is left-right symmetric; 3) 
               the numbers in each of the border rows, after the first 3, are alternately 
               0.
%F A085737 T(n, 0) = (-1)^n*Bernoulli(n), T(n, k) = T(n-1, k-1) + T(n, k-1) for 
               k=1..n.
%e A085737 Triangle begins
%e A085737 1
%e A085737 1/2, 1/2
%e A085737 1/6, 1/3, 1/6
%e A085737 0, 1/6, 1/6, 0
%e A085737 -1/30, 1/30, 2/15, 1/30, -1/30
%e A085737 0, -1/30, 1/15, 1/15, -1/30, 0
%e A085737 1/42, -1/42, -1/105, 8/105, -1/105, -1/42, 1/42
%e A085737 0, 1/42, -1/21, 4/105, 4/105, -1/21, 1/42, 0
%e A085737 -1/30, 1/30, -1/105, -4/105, 8/105, -4/105, -1/105, 1/30, -1/30
%Y A085737 Cf. A085738. See A051714/A051715 for another triangle that generates 
               the Bernoulli numbers.
%Y A085737 Sequence in context: A037800 A144411 A138253 this_sequence A005090 A073490 
               A135341
%Y A085737 Adjacent sequences: A085734 A085735 A085736 this_sequence A085738 A085739 
               A085740
%K A085737 sign,frac
%O A085737 0,13
%A A085737 N. J. A. Sloane (njas(AT)research.att.com), following a suggestion of 
               J. H. Conway, Jul 23 2003