A202205 G.f.: Sum_{n>=1} x^n * Product_{k=1..n} (1-x^k)^2.

1, 1, -1, 0, -2, 2, -1, 1, 2, -1, -1, 2, -1, -4, 3, -1, 0, -1, 0, 3, 1, -2, 0, 1, 3, -2, -3, 2, -2, 1, -1, 2, -4, -2, 5, -1, 1, 1, -4, 4, -1, 2, 1, -2, 2, -1, -1, -3, 3, 2, -1, -4, 0, 0, -1, 2, -1, 0, 2, -1, 0, -3, 5, -2, -1, 5, 3, -4, -2, 2, -4, 4, 0, 3, -2

Offset

0,5

Comments

Compare g.f. to: (1 - eta(x))/x = Sum_{n>=0} x^n*Product_{k=1..n} (1-x^k) = 1 + x - x^4 - x^6 + x^11 + x^14 - x^21 - x^25 + x^34 + x^39 +..., where eta(q) is the Dedekind eta function without the q^(1/24) factor.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + x - x^2 - 2*x^4 + 2*x^5 - x^6 + x^7 + 2*x^8 - x^9 - x^10 +...
where A(x) = 1 + x*(1-x)^2 + x^2*(1-x)^2*(1-x^2)^2 + x^3*(1-x)^2*(1-x^2)^2*(1-x^3)^2 +...

Mathematica

Join[{1}, Rest[CoefficientList[Series[Sum[x^n Product[(1-x^k)^2, {k, n}], {n, 100}], {x, 0, 100}], x]]] (* Harvey P. Dale, Jun 02 2024 *)

Prog

(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^m*prod(k=1, m, (1-x^k +x*O(x^n))^2)), n)}

Crossrefs

Cf. A202204.

Sequence in context: A264119 A225518 A269972 * A374034 A336123 A353849

Adjacent sequences: A202202 A202203 A202204 * A202206 A202207 A202208

Keyword

sign

Author

Paul D. Hanna, Dec 14 2011

Status

approved