A094363 Expansion of (eta(q) * eta(q^39)) / (eta(q^3) * eta(q^13)) in powers of q.

1, -1, -1, 1, -1, 0, 2, -1, -1, 3, -2, -1, 4, -2, -3, 4, -3, -3, 8, -4, -5, 9, -4, -6, 13, -6, -7, 14, -10, -9, 20, -9, -12, 24, -13, -13, 32, -16, -19, 39, -23, -24, 50, -26, -27, 60, -35, -34, 78, -41, -42, 91, -49, -54, 111, -60, -65, 138, -73, -78, 167, -84, -95, 199, -107, -111, 236, -128, -135, 282, -147, -159, 338

Offset

1,7

Links

Table of n, a(n) for n=1..73.

Formula

Euler transform of period 39 sequence [ -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, ...].

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) = f(1/A(x), 1/A(x^2)) where f(u, v)=u^3 + v^3 + 2*u*v*(u + v) - u^2*v^2 - u*v.

G.f.: x * Product_{k>0} (1 - x^k) * (1 - x^(3*9k)) / ((1 - x^(3*k)) * (1 - x^(13*k))).

Convolution inverse of A094362.

Example

q - q^2 - q^3 + q^4 - q^5 + 2*q^7 - q^8 - q^9 + 3*q^10 - 2*q^11 - q^12 + 4*q^13 + ...

Prog

(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^39 + A) / (eta(x^3 + A) * eta(x^13 + A)), n))}

Crossrefs

Cf. A094362.

Sequence in context: A079673 A124829 A093394 * A124832 A226130 A137569

Adjacent sequences: A094360 A094361 A094362 * A094364 A094365 A094366

Keyword

sign

Author

Michael Somos, May 03 2004

Status

approved