A327487 T(n, k) are the summands given by the generating function of A327420(n), triangle read by rows, T(n,k) for 0 <= k <= n.

1, 2, -2, 3, -3, 2, 4, -4, 3, 0, 5, -5, 4, 0, 2, 6, -6, 5, 0, 0, 0, 7, -7, 6, 0, 0, 3, 0, 8, -8, 7, 0, 0, 0, 0, 0, 9, -9, 8, 0, 0, 0, 4, 3, 0, 10, -10, 9, 0, 0, 0, 0, 0, -3, -2, 11, -11, 10, 0, 0, 0, 0, 5, 0, -3, 2, 12, -12, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Peter Luschny, Sep 14 2019

Keywords

• sign
• tabl

Examples

			Triangle starts (at the end of the line is the row sum (A327420)):
[ 0] [ 1] 1
[ 1] [ 2,  -2] 0
[ 2] [ 3,  -3,  2] 2
[ 3] [ 4,  -4,  3, 0] 3
[ 4] [ 5,  -5,  4, 0, 2] 6
[ 5] [ 6,  -6,  5, 0, 0, 0] 5
[ 6] [ 7,  -7,  6, 0, 0, 3, 0] 9
[ 7] [ 8,  -8,  7, 0, 0, 0, 0, 0] 7
[ 8] [ 9,  -9,  8, 0, 0, 0, 4, 3,  0] 15
[ 9] [10, -10,  9, 0, 0, 0, 0, 0, -3, -2] 4
[10] [11, -11, 10, 0, 0, 0, 0, 5,  0, -3, 2] 14
		

Crossrefs

Cf. A327420, A327093, A057032, A069829.

Programs

SageMath

def divsign(s, k):
    if not k.divides(s): return 0
    return (-1)^(s//k)*k
def A327487row(n):
    s = n + 1
    r = srange(s, 1, -1)
    S = [-divsign(s, s)]
    for k in r:
        s += divsign(s, k)
        S.append(-divsign(s, k))
    return S
# Prints the triangle like in the example section.
for n in (0..10):
    print([n], A327487row(n), sum(A327487row(n)))

Formula

Sum_{k=0..n} T(n, k) = A327420(n).