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A231947 Expansion of q^(-1/3) * a(q)^2 * c(q) / 3 in powers of q where a(), c() are cubic AGM theta functions. 4
1, 13, 50, 72, 170, 205, 362, 360, 601, 650, 962, 864, 1370, 1224, 1850, 1584, 2451, 2210, 2880, 2520, 3722, 3277, 4490, 3600, 5330, 4706, 6242, 5040, 6912, 6120, 8500, 6624, 9410, 7813, 10610, 8424, 11882, 10250, 12672, 10440, 14521, 12506, 16130, 12240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 q^(-1/3) * (eta(q)^3 + 9 * eta(q^9)^3)^2 * eta(q^3) / eta(q) in powers of q.

G.f. is a period 1 Fourier series which satisfies f(-1 / (9 t)) = 3^(1/2) (t/i)^3 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A231948.

-9 * a(n) = A109041(3*n + 1).

EXAMPLE

G.f. = 1 + 13*x + 50*x^2 + 72*x^3 + 170*x^4 + 205*x^5 + 362*x^6 + 360*x^7 + ...

G.f. = q + 13*q^4 + 50*q^7 + 72*q^10 + 170*q^13 + 205*q^16 + 362*q^19 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-1/3)*(eta[q]^3 + 9*eta[q^9]^3)^2*eta[q^3]/eta[q], {q, 0, 50}], q] (* G. C. Greubel, Aug 08 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^3 + 9 * x * eta(x^9 + A)^3)^2 * eta(x^3 + A) / eta(x + A), n))}

CROSSREFS

Cf. A109041, A231948.

Sequence in context: A274784 A294520 A189054 * A209995 A050410 A121991

Adjacent sequences:  A231944 A231945 A231946 * A231948 A231949 A231950

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 15 2013

STATUS

approved

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Last modified October 23 18:46 EDT 2018. Contains 316530 sequences. (Running on oeis4.)