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A227396
Triangle A074909(n) with the first column equal to 1 followed by -A000027(n) instead of A000012.
0
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
0,3
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).
FORMULA
T(n,k) = A074909(n,k) for n>0 and k>0, T(0,0)=1, T(n,0)=-n for n>0.
EXAMPLE
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.
CROSSREFS
Sequence in context: A376695 A173910 A036846 * A331590 A326496 A058740
KEYWORD
sign,tabl
AUTHOR
Paul Curtz, Sep 20 2013
STATUS
approved