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A215556 Expansion of q * psi(-q) * phi(q) * psi(-q^7) in powers of q where phi(), psi() are Ramanujan theta functions. 2
1, 1, -2, -1, 0, -2, 1, -1, -1, 4, 2, 2, 0, -1, 2, 1, -2, -3, -2, 0, 0, -4, -2, 2, 1, 0, 4, -1, 0, 2, -4, 1, 0, 2, 0, 1, 0, 2, 2, -4, 2, 0, 2, -2, 0, 2, 0, -2, 1, -1, -4, 0, 0, 4, -4, 1, -2, -2, 2, -2, 0, 0, -1, -1, 2, -4, -2, 2, 0, 0, 0, 3, 2, -2, 2, 2, 0, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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..5000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of eta(q^2)^4 * eta(q^7) * eta(q^28) / (eta(q) * eta(q^4) * eta(q^14)) in powers of q.

Euler transform of period 28 sequence [ 1, -3, 1, -2, 1, -3, 0, -2, 1, -3, 1, -2, 1, -3, 1, -2, 1, -3, 1, -2, 0, -3, 1, -2, 1, -3, 1, -3, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (28 t)) = 392^(1/2) (t/i)^(3/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A159813.

a(7*n) = A159813(n).

EXAMPLE

G.f. = q + q^2 - 2*q^3 - q^4 - 2*q^6 + q^7 - q^8 - q^9 + 4*q^10 + 2*q^11 + 2*q^12 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 2, Pi/4, q^(1/2)] EllipticTheta[ 2, Pi/4, q^(7/2)] / 2, {q, 0, n}]; (* Michael Somos, Aug 27 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^7 + A) * eta(x^28 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^14 + A)), n))};

CROSSREFS

Cf. A159813.

Sequence in context: A270657 A270658 A117278 * A140082 A330714 A343640

Adjacent sequences:  A215553 A215554 A215555 * A215557 A215558 A215559

KEYWORD

sign

AUTHOR

Michael Somos, Aug 15 2012

STATUS

approved

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Last modified January 26 05:13 EST 2022. Contains 350572 sequences. (Running on oeis4.)