A274719 Expansion of Product_{k >= 1} (1-q^(2*k)).

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.

Links

Table of n, a(n) for n=0..102.

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

Cf. A000009, A010815, A035363, A089806.

Sequence in context: A014093 A373601 A089806 * A014069 A154388 A285136

Adjacent sequences: A274716 A274717 A274718 * A274720 A274721 A274722

Keyword

sign

Author

George Beck, Jul 03 2016

Extensions

Simpler definition from N. J. A. Sloane, Mar 24 2018

Status

approved