A182038 Expansion of eta(q) * eta(q^36) / (eta(q^4) * eta(q^9)) in powers of q.

1, -1, -1, 0, 1, 0, -1, 1, 2, 0, -3, 0, 2, 0, -3, 0, 5, 0, -4, -2, 4, 0, -5, 0, 7, 2, -7, 0, 5, 0, -10, 1, 12, 0, -10, 0, 14, -4, -17, 0, 21, 0, -22, 4, 24, 0, -34, 0, 33, 1, -36, 0, 45, 0, -45, -8, 52, 0, -55, 0, 62, 8, -71, 0, 70, 0, -88, 2, 96, 0, -98, 0

Offset

1,9

Links

G. C. Greubel, Table of n, a(n) for n = 1..2500

Formula

Euler transform of period 36 sequence [-1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 Pi i t).

G.f.: Product_{k>0} (1 - x^k) * (1 - x^(36*k)) / ((1 - x^(4*k)) * (1 - x^9*k)).

a(6*n) = a(6*n + 4) = 0. a(6*n + 2) = -A092848(n).

Convolution inverse of A187020.

Example

G.f. = q - q^2 - q^3 + q^5 - q^7 + q^8 + 2*q^9 - 3*q^11 + 2*q^13 - 3*q^15 + ...

Mathematica

QP = QPochhammer; s = QP[q]*(QP[q^36]/(QP[q^4]*QP[q^9])) + O[q]^80; CoefficientList[s, q]

Prog

(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^36 + A) / (eta(x^4 + A) * eta(x^9 + A)), n))};

Crossrefs

Cf. A092848, A187020. Essentially the same as A213266.

Sequence in context: A336124 A256580 A213266 * A128144 A128145 A128143

Adjacent sequences: A182035 A182036 A182037 * A182039 A182040 A182041

Keyword

sign

Author

Michael Somos, Apr 07 2012

Status

approved