A227396 Triangle A074909(n) with the first column equal to 1 followed by -A000027(n) instead of A000012.

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, 7, -7, 8, 28, 56, 70, 56, 28, 8, -8, 9, 36, 84, 126, 126, 84, 36, 9, -9, 10, 45, 120, 210, 252, 210, 120, 45, 10, -10

Offset: 0

Author

Paul Curtz, Sep 20 2013

Keywords

• sign
• tabl

Comments

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

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

1*B(0) = 1

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

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

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

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

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

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

Examples

			a(n) triangle is A:
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 7  etc.
		

Formula

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