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A181648 Expansion of x^(-2/3) * psi(x) * c(x^2) / 3 in powers of x where psi() is a Ramanujan theta function and c() is a cubic AGM theta function. 4
1, 1, 1, 2, 2, 3, 1, 2, 3, 2, 4, 3, 3, 3, 4, 3, 2, 2, 6, 5, 3, 5, 3, 5, 4, 5, 3, 4, 5, 4, 5, 4, 5, 7, 6, 7, 3, 3, 7, 4, 8, 4, 4, 5, 7, 6, 5, 6, 7, 8, 6, 4, 6, 9, 6, 8, 6, 4, 4, 4, 11, 7, 4, 11, 4, 9, 6, 7, 8, 7, 11, 5, 5, 8, 8, 10, 6, 5, 10, 6, 8, 6, 7, 7, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-19/24) * eta(q^2) * eta(q^6)^3 / eta(q) in powers of q.

Euler transform of period 6 sequence [ 1, 0, 1, 0, 1, -3, ...].

3 * a(n) = A008443(3*n + 2).

EXAMPLE

1 + x + x^2 + 2*x^3 + 2*x^4 + 3*x^5 + x^6 + 2*x^7 + 3*x^8 + 2*x^9 + 4*x^10 + ...

q^19 + q^43 + q^67 + 2*q^91 + 2*q^115 + 3*q^139 + q^163 + 2*q^187 + 3*q^211 + ...

MATHEMATICA

A181648[n_]:= SeriesCoefficient[QPochhammer[q^2, q^2]*QPochhammer[q^6, q^6]^3/QPochhammer[q, q], {q, 0, n}]; Table[A181648[n], {n, 0, 50}] (* G. C. Greubel, Dec 24 2017 *)

PROG

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

CROSSREFS

Cf. A008443.

Sequence in context: A284051 A226743 A166269 * A182910 A055460 A067514

Adjacent sequences:  A181645 A181646 A181647 * A181649 A181650 A181651

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 22 2012

STATUS

approved

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Last modified September 15 18:47 EDT 2019. Contains 327083 sequences. (Running on oeis4.)