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A078616
a(n) = Sum_{k=0..n} A010815(k).
7
1, 0, -1, -1, -1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
0,1
COMMENTS
To construct the sequence: a(0)=1, a(1)=0, then (2*1+1) (-1)'s followed by 2 0's, followed by (2*2+1) 1's, followed by 3 0's, followed by (2*3+1) (-1)'s, etc.
From George Beck, May 05 2017: (Start)
a(n) = (Number of ones in the distinct partitions of n with an odd number of parts) - (number of ones in the distinct partitions of n with an even number of parts) (conjectured).
The partial sums give A246575. (End) [corrected by Ilya Gutkovskiy, Aug 18 2018]
FORMULA
For m > 0, a(k)=0 if A000326(m) <= k < A000326(m) + m; a(k)=(-1)^m if A000326(m) + m <= k < A000326(m+1).
G.f.: eta(x)/(1-x). - Benoit Cloitre, Jan 31 2004
G.f.: exp(-Sum_{k>=1} (sigma_1(k) - 1)*x^k/k). - Ilya Gutkovskiy, Aug 18 2018
PROG
(PARI) a(n)=polcoeff(eta(x)/(1-x)+O(x^n), n)
CROSSREFS
KEYWORD
sign
AUTHOR
Benoit Cloitre, Dec 10 2002
STATUS
approved