A227396 - OEIS

%I #23 Oct 05 2013 04:44:44

%S 1,-1,2,-2,3,3,-3,4,6,4,-4,5,10,10,5,-5,6,15,20,15,6,-6,7,21,35,35,21,

%T 7,-7,8,28,56,70,56,28,8,-8,9,36,84,126,126,84,36,9,-9,10,45,120,210,

%U 252,210,120,45,10,-10

%N Triangle A074909(n) with the first column equal to 1 followed by -A000027(n) instead of A000012.

%C Triangle leading to A164555(n)/A027642(n).

%C Starting from B(0)=1, the Bernoulli numbers B(n) with B(1)=1/2 are such that

%C 1*B(0) = 1

%C -1*B(0) +2*B(1)= 0                               --> B(1)=1/2

%C -2*B(0) +3*B(1)  +3*B(2) = 0                     --> B(2)=1/6

%C -3*B(0) +4*B(1)  +6*B(2) +4*B(3) = 0             --> B(3)=0

%C -4*B(0) +5*B(1) +10*B(2) +10*B(3) +5*B(4) = 0    --> B(4)=-1/30 etc.

%C Row sum of A: A130103(n+1).

%C Row sum's absolute values of A: A145071(n).

%F T(n,k) = A074909(n,k) for n>0 and k>0, T(0,0)=1, T(n,0)=-n for n>0.

%e a(n) triangle is A:

%e 1

%e -1 2

%e -2 3  3

%e -3 4  6  4

%e -4 5 10 10  5

%e -5 6 15 20 15  6

%e -6 7 21 35 35 21 7  etc.

%K sign,tabl

%O 0,3

%A _Paul Curtz_, Sep 20 2013