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A227033 Expansion of (phi(x) / f(-x^4))^2 in powers of x where phi(), f() are Ramanujan theta functions. 2
1, 4, 4, 0, 6, 16, 8, 0, 17, 40, 28, 0, 38, 96, 56, 0, 84, 204, 124, 0, 172, 400, 232, 0, 325, 760, 448, 0, 594, 1376, 784, 0, 1049, 2404, 1388, 0, 1796, 4096, 2320, 0, 3005, 6808, 3864, 0, 4912, 11072, 6216, 0, 7877, 17688, 9940, 0, 12430, 27792, 15488, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 (terms 0..55 from Michael Somos)

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(1/3) * (eta(q^2)^5 / (eta(q)^2 * eta(q^4)^3))^2 in powers of q.

Euler transform of period 4 sequence [4, -6, 4, 0, ...].

a(4*n + 3) = 0. a(2*n) = A112160(n). a(4*n + 1) = 4 * A022569(n).

EXAMPLE

G.f. = 1 + 4*x + 4*x^2 + 6*x^4 + 16*x^5 + 8*x^6 + 17*x^8 + 40*x^9 + 28*x^10 + ...

G.f. = 1/q + 4*q^2 + 4*q^5 + 6*q^11 + 16*q^14 + 8*q^17 + 17*q^23 + 40*q^26 + ...

MATHEMATICA

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

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 / (eta(x + A)^2 * eta(x^4 + A)^3))^2, n))};

CROSSREFS

Cf. A022569, A112160.

Sequence in context: A169783 A133657 A121455 * A285050 A262949 A200519

Adjacent sequences:  A227030 A227031 A227032 * A227034 A227035 A227036

KEYWORD

nonn

AUTHOR

Michael Somos, Jul 03 2013

STATUS

approved

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Last modified December 12 03:17 EST 2018. Contains 318052 sequences. (Running on oeis4.)