A297054 The coefficients of the product (1-x^2)(1-x^3)(1-x^4)... / (1+x).

1, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, -1, 1, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, -1, 1, -1, 1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0

Offset

0

Links

Table of n, a(n) for n=0..87.

Formula

From Seiichi Manyama, Apr 11 2025: (Start)

G.f.: 1/(1-x^2) * Product_{k>=1} (1-x^k).

a(n) = Sum_{k=0..floor(n/2)} A010815(n-2*k). (End)

Mathematica

iend = 100;
s = Series[1/(1 + x) Product[(1 - x^i), {i, 2, iend}], {x, 0, iend}];
Print[s]; Print[CoefficientList[s, x]]

Prog

(PARI) first(n) = Vec(prod(i=2, n-1, 1 - x^i)/(1 + x) + O(x^n)) \\ Iain Fox, Dec 24 2017

Crossrefs

Cf. A010815, A078616.

Sequence in context: A379274 A321512 A373489 * A359349 A266459 A354199

Adjacent sequences: A297051 A297052 A297053 * A297055 A297056 A297057

Keyword

sign

Author

David S. Newman, Dec 24 2017

Extensions

Offset changed to 0 by Seiichi Manyama, Apr 11 2025

Status

approved