A131018 Expansion of (q^-3) * psi(q) / psi(q^25) in powers of q where psi() is a Ramanujan theta function.

1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -2, -2, 0, 0, 0, -1, -2, 0

Offset

-3,76

Comments

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

References

F. Calegari, Review of "A first Course in modular forms" by F. Diamond and J. Shurman, Bull. Amer. Math. Soc., 43 (No. 3, 2006), 415-421. See p. 418

Links

G. C. Greubel, Table of n, a(n) for n = -3..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

G.f.: (x^-3) * Product_{k>0} (1 - x^k) * (1 + x^k)^2 / ((1 - x^(25*k)) * (1 + x^(50*k))^2).

Example

G.f. = q^-3 + q^-2 + 1 + q^3 + q^7 + q^12 + q^18 - q^22 - q^23 - q^28 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q^(1/2)] / EllipticTheta[ 2, 0, q^(25/2)], {q, 0, n}]; (* Michael Somos, Nov 11 2015 *)
a[ n_] := SeriesCoefficient[ q^-3 QPochhammer[ q^2]^2 QPochhammer[ q^25] / (QPochhammer[ q] QPochhammer[ q^50]), {q, 0, n}]; (* Michael Somos, Nov 11 2015 *)

Prog

(PARI) {a(n) = my(A); if( n<-3, 0, n+=3; A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^25 + A) / (eta(x + A) * eta(x^50 + A)^2), n))};

Crossrefs

Sequence in context: A049800 A281082 A204421 * A300067 A035395 A116856

Adjacent sequences: A131015 A131016 A131017 * A131019 A131020 A131021

Keyword

sign

Author

Michael Somos, Jun 10 2007

Status

approved