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A145727 Expansion of f(q) * f(q^15) / (f(-q^6) * f(-q^10)) in powers of q where f() is a Ramanujan theta function. 4
1, 1, -1, 0, 0, -1, 1, 0, -1, 0, 1, 0, 0, 1, -2, 1, 2, -3, 1, 1, -2, 3, 0, -3, 1, 2, -2, 0, 2, -6, 3, 4, -7, 3, 2, -5, 6, 2, -8, 3, 5, -6, 2, 4, -12, 7, 10, -15, 6, 5, -13, 12, 4, -18, 7, 11, -14, 6, 10, -24, 14, 20, -32, 12, 12, -29, 24, 9, -36, 15, 22, -30 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,15

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of (eta(q^2) * eta(q^30))^3 / (eta(q) * eta(q^4) * eta(q^6) * eta(q^10) * eta(q^15) * eta(q^60)) in powers of q.

Euler transform of a period 60 sequence.

G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 Pi i t).

a(n) = A145726(n) unless n=0. Convolution inverse of A145728.

EXAMPLE

G.f. = 1 + q - q^2 - q^5 + q^6 - q^8 + q^10 + q^13 - 2*q^14 + q^15 + 2*q^16 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -q] QPochhammer[ -q^15] / (QPochhammer[ q^6] QPochhammer[ q^10]), {q, 0, n}]; (* Michael Somos, Sep 05 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^30 + A))^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A) * eta(x^60 + A)), n))};

CROSSREFS

Cf. A145726, A145728.

Sequence in context: A336320 A145782 A131797 * A131796 A131794 A145726

Adjacent sequences:  A145724 A145725 A145726 * A145728 A145729 A145730

KEYWORD

sign

AUTHOR

Michael Somos, Oct 23 2008

STATUS

approved

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Last modified June 13 16:09 EDT 2021. Contains 345008 sequences. (Running on oeis4.)