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A139214 Expansion of q * psi(q^2) * psi(-q^9) / (phi(-q^3) * psi(-q^3)) in powers of q where phi(), psi() are Ramanujan theta functions. 7
1, 0, 1, 3, 0, 3, 8, 0, 7, 18, 0, 15, 38, 0, 30, 75, 0, 57, 140, 0, 104, 252, 0, 183, 439, 0, 313, 744, 0, 522, 1232, 0, 852, 1998, 0, 1365, 3182, 0, 2150, 4986, 0, 3336, 7700, 0, 5106, 11736, 0, 7719, 17673, 0, 11538, 26322, 0, 17067, 38808, 0, 25004, 56682, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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 = 1..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of eta(q^4)^2 * eta(q^6)^2 * eta(q^9) * eta(q^36) / (eta(q^2) * eta(q^3)^3 * eta(q^12) * eta(q^18)) in powers of q.

G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = (1/4) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A139216.

a(3*n + 2) = 0. 2 * a(n) = A139213(n) unless n=0.

a(3*n) = A187100(n). a(2*n + 4) = 3 * A261992(n). - Michael Somos, Sep 07 2015

EXAMPLE

G.f. = q + q^3 + 3*q^4 + 3*q^6 + 8*q^7 + 7*q^9 + 18*q^10 + 15*q^12 + 38*q^13 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[(1/2) EllipticTheta[ 2, 0, q] EllipticTheta[ 2, Pi/4, q^(9/2)] / (EllipticTheta[ 4, 0, q^3] EllipticTheta[ 2, Pi/4, q^(3/2)]), {q, 0, n}]; (* Michael Somos, Sep 07 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^4 + A)^2 * eta(x^6 + A)^2 * eta(x^9 + A) * eta(x^36 + A) / (eta(x^2 + A) * eta(x^3 + A)^3 * eta(x^12 + A) * eta(x^18 + A)), n))};

CROSSREFS

Cf. A139213, A139216, A187100, A261992.

Sequence in context: A127803 A021771 A154853 * A010030 A197270 A117940

Adjacent sequences:  A139211 A139212 A139213 * A139215 A139216 A139217

KEYWORD

nonn

AUTHOR

Michael Somos, Apr 11 2008

STATUS

approved

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Last modified February 23 10:56 EST 2018. Contains 299536 sequences. (Running on oeis4.)