A182033 Expansion of c(q^2)^2 / (c(q) * c(q^6)) in powers of q where c() is a cubic AGM theta function.

1, -1, 1, 1, 0, -1, 1, 0, 0, -1, 0, 2, -1, 0, -2, 0, 0, -1, 1, 0, 4, 2, 0, -4, 0, 0, -1, -2, 0, 8, -3, 0, -8, -1, 0, -2, 4, 0, 14, 4, 0, -14, 1, 0, -4, -4, 0, 24, -6, 0, -23, -1, 0, -6, 5, 0, 40, 8, 0, -38, 1, 0, -10, -8, 0, 63, -10, 0, -60, -2, 0, -16, 11

Offset

-1,12

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

Formula

Expansion of eta(q) * eta(q^6)^7 / (eta(q^2)^2 * eta(q^3)^3 * eta(q^18)^3) in powers of q.

Euler transform of period 18 sequence [ -1, 1, 2, 1, -1, -3, -1, 1, 2, 1, -1, -3, -1, 1, 2, 1, -1, 0, ...].

a(3*n) = 0 unless n=0. a(3*n + 1) = a(6*n + 2) = A092848(n). a(3*n + 2) = A062242(n). a(6*n + 4) = a(12*n + 8) = - A164614(n). a(6*n + 5) = A132179(n).

Convolution inverse of A122830.

Example

1/q - 1 + q + q^2 - q^4 + q^5 - q^8 + 2*q^10 - q^11 - 2*q^13 - q^16 + ...

Mathematica

eta[x_] := x^(1/24)*QPochhammer[x]; A182033[n_] := SeriesCoefficient[ eta[q]*eta[q^6]^7/(eta[q^2]^2*eta[q^3]^3*eta[q^18]^3 ), {q, 0, n}]; Table[A182033[n], {n, -1, 50}] (* G. C. Greubel, Aug 18 2017 *)

Prog

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^7 / (eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^18 + A)^3), n))}

Crossrefs

Cf. A062242, A092848, A122830, A133179, A164614.

Sequence in context: A228817 A110399 A193275 * A112214 A246962 A112608

Adjacent sequences: A182030 A182031 A182032 * A182034 A182035 A182036

Keyword

sign

Author

Michael Somos, Apr 07 2012

Status

approved