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A181976 Expansion of a(q) * b(q)^2 in powers of q where a(), b() are cubic AGM theta functions. 2
1, 0, -27, 72, 0, -216, 270, 0, -459, 720, 0, -1080, 936, 0, -1350, 2160, 0, -2592, 2214, 0, -2808, 3600, 0, -4752, 4590, 0, -4590, 6552, 0, -7560, 5184, 0, -7371, 10800, 0, -10800, 9360, 0, -9774, 12240, 0, -15120, 13500, 0, -14040, 17712, 0, -19872, 14760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

FORMULA

Expansion of b(q^3)^3 - 3 * b(q) * c(q^3)^2 in powers of q where b(), c() are cubic AGM theta functions.

Expansion of b(q^3)^2 * (b(q) + c(q^3)) in powers of q^3 where b(), c() are cubic AGM theta functions.

Expansion of (eta(q)^9 + 9 * q * eta(q)^6 * eta(q^9)^3) / eta(q^3)^3 in powers of q.

a(3*n + 1) = 0. a(3*n) = A004007(n).

EXAMPLE

G.f. = 1 - 27*q^2 + 72*q^3 - 216*q^5 + 270*q^6 - 459*q^8 + 720*q^9 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]^9 + 9*q*eta[q]^6*eta[q^9]^3)/eta[q^3]^3, {q, 0, 50}], q] (* G. C. Greubel, Aug 11 2018 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^9 + 9 * x * eta(x + A)^6 * eta(x^9 + A)^3) / eta(x^3 + A)^3, n))};

CROSSREFS

Cf. A004007.

Sequence in context: A224525 A219130 A116302 * A039414 A043237 A044017

Adjacent sequences:  A181973 A181974 A181975 * A181977 A181978 A181979

KEYWORD

sign

AUTHOR

Michael Somos, Apr 04 2012

STATUS

approved

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Last modified March 7 09:46 EST 2021. Contains 341869 sequences. (Running on oeis4.)