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A263452 Expansion of f(-q^3)^3 * psi(q^12) / f(-q) in powers of q where ps(), f() are Ramanujan theta functions. 3
1, 1, 2, 0, 2, 1, 2, 0, 1, 2, 2, 0, 3, 1, 4, 0, 5, 3, 2, 0, 3, 3, 4, 0, 4, 2, 4, 0, 3, 2, 4, 0, 4, 2, 4, 0, 5, 5, 4, 0, 3, 3, 8, 0, 7, 3, 6, 0, 4, 4, 4, 0, 6, 4, 4, 0, 9, 3, 6, 0, 4, 4, 4, 0, 4, 3, 8, 0, 5, 5, 6, 0, 9, 3, 4, 0, 7, 6, 6, 0, 7, 6, 10, 0, 6, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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..2500

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-11/6) * eta(q^3)^3 * eta(q^24)^2 / (eta(q) * eta(q^12)) in powers of q.

Euler transform of period 24 sequence [ 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -1, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -3, ...].

2 * a(n) = A261444(2*n + 1).  a(4*n + 1) = A212907(n). a(4*n + 3) = 0.

-2 * a(n) = A263527(2*n + 3). - Michael Somos, Nov 05 2015

EXAMPLE

G.f. = 1 + x + 2*x^2 + 2*x^4 + x^5 + 2*x^6 + x^8 + 2*x^9 + 2*x^10 + ...

G.f. = q^11 + q^17 + 2*q^23 + 2*q^35 + q^41 + 2*q^47 + q^59 + 2*q^65 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ q^3]^3 EllipticTheta[ 2, 0, q^6] / ( 2 q^(3/2) QPochhammer[ q]), {q, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^3 * eta(x^24 + A)^2 / (eta(x + A) * eta(x^12 + A)), n))};

CROSSREFS

Cf. A212907, A261444, A263527.

Sequence in context: A219762 A227696 A033687 * A133457 A324120 A218857

Adjacent sequences:  A263449 A263450 A263451 * A263453 A263454 A263455

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 18 2015

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)