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A274719
Expansion of Product_{k >= 1} (1-q^(2*k)).
4
1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
0
COMMENTS
Convolution of A000009 and A010815.
FORMULA
Equals convolution inverse of A035363.
a(2n) = A010815(n).
Conjecture: |a(n)| = A089806(n).
EXAMPLE
G.f. = 1 - x^2 - x^4 + x^10 + x^14 - x^24 - x^30 + x^44 + x^52 - x^70 - ... - Altug Alkan, Mar 24 2018
MATHEMATICA
nmax = 100; CoefficientList[ Series[Product[(1 - x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 05 2016 *)
PROG
(PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q^2))} \\ Altug Alkan, Mar 21 2018
CROSSREFS
KEYWORD
sign
AUTHOR
George Beck, Jul 03 2016
EXTENSIONS
Simpler definition from N. J. A. Sloane, Mar 24 2018
STATUS
approved