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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.

%I A327487 #23 Feb 29 2020 04:21:28
%S A327487 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,
%T A327487 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,
%U A327487 0,0,5,0,-3,2,12,-12,11,0,0,0,0,0,0,0,0,0
%N 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.
%F A327487 Sum_{k=0..n} T(n, k) = A327420(n).
%e A327487 Triangle starts (at the end of the line is the row sum (A327420)):
%e A327487 [ 0] [ 1] 1
%e A327487 [ 1] [ 2,  -2] 0
%e A327487 [ 2] [ 3,  -3,  2] 2
%e A327487 [ 3] [ 4,  -4,  3, 0] 3
%e A327487 [ 4] [ 5,  -5,  4, 0, 2] 6
%e A327487 [ 5] [ 6,  -6,  5, 0, 0, 0] 5
%e A327487 [ 6] [ 7,  -7,  6, 0, 0, 3, 0] 9
%e A327487 [ 7] [ 8,  -8,  7, 0, 0, 0, 0, 0] 7
%e A327487 [ 8] [ 9,  -9,  8, 0, 0, 0, 4, 3,  0] 15
%e A327487 [ 9] [10, -10,  9, 0, 0, 0, 0, 0, -3, -2] 4
%e A327487 [10] [11, -11, 10, 0, 0, 0, 0, 5,  0, -3, 2] 14
%o A327487 (SageMath)
%o A327487 def divsign(s, k):
%o A327487     if not k.divides(s): return 0
%o A327487     return (-1)^(s//k)*k
%o A327487 def A327487row(n):
%o A327487     s = n + 1
%o A327487     r = srange(s, 1, -1)
%o A327487     S = [-divsign(s, s)]
%o A327487     for k in r:
%o A327487         s += divsign(s, k)
%o A327487         S.append(-divsign(s, k))
%o A327487     return S
%o A327487 # Prints the triangle like in the example section.
%o A327487 for n in (0..10):
%o A327487     print([n], A327487row(n), sum(A327487row(n)))
%Y A327487 Cf. A327420, A327093, A057032, A069829.
%K A327487 sign,tabl
%O A327487 0,2
%A A327487 _Peter Luschny_, Sep 14 2019