A202204 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1-x^k)^3.

1, 1, -2, 1, -3, 6, -3, 0, 5, -7, -4, 9, -1, -13, 14, 3, -1, -7, -6, 19, -3, -13, -9, 4, 24, -6, -20, 8, -6, 18, 7, 7, -27, -30, 41, 1, 15, -9, -35, 1, -9, 39, 18, -21, 12, -25, -24, -8, 49, 41, 5, -51, -37, 1, -18, 61, 8, 16, 3, -33, -40, -49, 52, 26, 14, 53, 32

Offset

0,3

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..1001

Example

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

Prog

(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^m*prod(k=1, m, (1-x^k +x*O(x^n))^3)), n)}

Crossrefs

Cf. A202205.

Sequence in context: A335444 A358646 A006895 * A289815 A125205 A125206

Adjacent sequences: A202201 A202202 A202203 * A202205 A202206 A202207

Keyword

sign

Author

Paul D. Hanna, Dec 14 2011

Status

approved