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A261877 Expansion of psi(x^4) / phi(-x^3) in powers of x where phi(), psi() are Ramanujan theta functions. 3
1, 0, 0, 2, 1, 0, 4, 2, 0, 8, 4, 0, 15, 8, 0, 26, 14, 0, 44, 24, 0, 72, 40, 0, 115, 64, 0, 180, 100, 0, 276, 154, 0, 416, 232, 0, 618, 344, 0, 906, 505, 0, 1312, 730, 0, 1880, 1044, 0, 2666, 1480, 0, 3746, 2076, 0, 5220, 2888, 0, 7216, 3988, 0, 9903, 5464, 0 (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..2500

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-1/2) * eta(q^6) * eta(q^8)^2 / (eta(q^3)^2 * eta(q^4)) in powers of q.

Euler transform of period 24 sequence [ 0, 0, 2, 1, 0, 1, 0, -1, 2, 0, 0, 2, 0, 0, 2, -1, 0, 1, 0, 1, 2, 0, 0, 0, ...].

2 * a(n) = A143068(2*n + 1). a(3*n + 2) = 0.

Convolution inverse is A262929. - Michael Somos, Oct 22 2017

EXAMPLE

G.f. = 1 + 2*x^3 + x^4 + 4*x^6 + 2*x^7 + 8*x^9 + 4*x^10 + 15*x^12 + ...

G.f. = q + 2*q^7 + q^9 + 4*q^13 + 2*q^15 + 8*q^19 + 4*q^21 + 15*q^25 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 1/2 (x^2)^(-1/4) EllipticTheta[ 2, 0, x^2] / EllipticTheta[ 4, 0, x^3], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^6 + A) * eta(x^8 + A)^2 / (eta(x^3 + A)^2 * eta(x^4 + A)), n))};

CROSSREFS

Cf. A143068, A262929.

Sequence in context: A139136 A122792 A138002 * A062296 A249343 A140649

Adjacent sequences:  A261874 A261875 A261876 * A261878 A261879 A261880

KEYWORD

nonn

AUTHOR

Michael Somos, Sep 09 2015

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)