A184366 G.f.: eta(x)^3*(1 - x*eta'(x)/eta(x)), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor.

1, -2, 0, 0, 0, 0, 7, 0, 0, 0, -21, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, -78, 0, 0, 0, 0, 0, 0, 125, 0, 0, 0, 0, 0, 0, 0, -187, 0, 0, 0, 0, 0, 0, 0, 0, 266, 0, 0, 0, 0, 0, 0, 0, 0, 0, -364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 483, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 792, 0, 0

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: A(x) = Sum_{n>=0} -(-1)^n * (n-2)(n+3)(2n+1)/6 * x^(n(n+1)/2).

Example

G.f.: A(x) = 1 - 2*x + 7*x^6 - 21*x^10 + 44*x^15 - 78*x^21 +...
A(x) = eta(x)^3*[1 - x*d/dx log(eta(x))] where
eta(x)^3 = 1 - 3*x + 5*x^3 - 7*x^6 + 9*x^10 - 11*x^15 +...+ (-1)^n*(2n+1)*x^(n(n+1)/2) +...
1 - x*d/dx log(eta(x)) = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + 6*x^5 + 12*x^6 + 8*x^7 + 15*x^8 +...+ sigma(n)*x^n +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, -(-1)^m*(m-2)*(m+3)*(2*m+1)/6*x^(m*(m+1)/2)), n)}
(PARI) {a(n)=polcoeff(eta(x+x*O(x^n))^3*(1-x*deriv(log(eta(x+x*O(x^n))))), n)}

Crossrefs

Cf. A000203, A184363, A184365, A283334.

Sequence in context: A107503 A350731 A364055 * A230614 A230730 A299905

Adjacent sequences: A184363 A184364 A184365 * A184367 A184368 A184369

Keyword

sign

Author

Paul D. Hanna, Jan 17 2011

Status

approved