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0, 1, 1, -1, -1, -3, 0, -2, 1, 2, 1, 2, 4, 1, -1, 4, -2, -1, -3, -1, -2, -2, -6, 0, -1, 1, -4, 0, 3, 2, 2, 2, 3, 0, 4, 7, 0, 0, 2, -3, 7, -2, -1, -3, -2, -4, 0, -3, -3, -2, -1, -10, -1, 0, 1, -1, 0, -6, 2, 2, 0, 4, 3, 4, 0, 2, 4, 3, 0, 5, 8, 2, 0, 1, -1, 1, -3
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OFFSET
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0,6
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COMMENTS
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Difference between the number of parts in all partitions of n into odd number of distinct parts and the number of parts in all partitions of n into even number of distinct parts.
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1-x^k) * Sum_{k>=1} x^k/(1-x^k).
G.f.: (x)_inf * (log(1-x) + psi_x(1))/log(x), where psi_q(z) is the q-digamma function, (q)_inf is the q-Pochhammer symbol (the Euler function).
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MAPLE
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add( numtheory[tau](k)*A010815(n-k), k=0..n) ;
# second Maple program:
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, [1, 0$3], b(n, i-1)+`if`(i>n, 0, (p->
[p[2], p[1], p[4]+p[2], p[3]+p[1]])(b(n-i, i-1)))))
end:
a:= n-> (p-> p[4]-p[3])(b(n$2)):
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MATHEMATICA
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Table[SeriesCoefficient[QPochhammer[x] (Log[1 - x] + QPolyGamma[1, x])/Log[x], {x, 0, n}], {n, 0, 80}] (* Vladimir Reshetnikov, Nov 20 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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