OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..500
EXAMPLE
a(0) = 1;
a(1) = [x^1] (1 - x) = -1;
a(2) = [x^2] (1 - x)^2*(1 - x^2) = 0;
a(3) = [x^3] (1 - x)^3*(1 - x^2)^2*(1 - x^3) = 4;
a(4) = [x^4] (1 - x)^4*(1 - x^2)^3*(1 - x^3)^2*(1 - x^4) = -7;
a(5) = [x^5] (1 - x)^5*(1 - x^2)^4*(1 - x^3)^3*(1 - x^4)^2*(1 - x^5) = 0, etc.
...
The table of coefficients of x^k in expansion of Product_{k=1..n} (1 - x^k)^(n-k+1) begins:
n = 0: (1), 0, 0, 0, 0, 0, ...
n = 1: 1, (-1), 0, 0, 0, 0, ...
n = 2: 1, -2, (0), 2, -1, 0, ...
n = 3: 1, -3, 1, (4), -2, -2, ...
n = 4: 1, -4, 3, 6, (-7), -2, ...
n = 5: 1, -5, 6, 7, -16, (0), ...
MATHEMATICA
Table[SeriesCoefficient[Product[(1 - x^k)^(n - k + 1), {k, 1, n}], {x, 0, n}], {n, 0, 33}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 19 2018
STATUS
approved