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A279270 Expansion of phi(-x) * chi(-x)^2 * f(-x^6)^3 in powers of x where phi(), chi(), f() are Ramanujan theta functions. 1
1, -4, 5, -4, 10, -16, 12, -8, 14, -28, 21, -8, 30, -40, 28, -16, 21, -52, 34, -20, 50, -56, 48, -24, 38, -72, 44, -28, 70, -88, 56, -24, 43, -100, 70, -36, 80, -112, 84, -32, 62, -104, 85, -44, 110, -136, 56, -56, 74, -148, 102, -40, 130, -144, 120, -56, 64 (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..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-2/3) * eta(q)^4 * eta(q^6)^3 / eta(q^2)^3 in powers of q.

Euler transform of period 6 sequence [ -4, -1, -4, -1, -4, -4, ...].

3 * a(n) = A260301(3*n + 2).

EXAMPLE

G.f. = 1 - 4*x + 5*x^2 - 4*x^3 + 10*x^4 - 16*x^5 + 12*x^6 - 8*x^7 + ...

G.f. = q^2 - 4*q^5 + 5*q^8 - 4*q^11 + 10*q^14 - 16*q^17 + 12*q^20 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x] QPochhammer[ x, x^2]^2 QPochhammer[ x^6]^3, {x, 0, n}];

PROG

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

CROSSREFS

Cf. A260301.

Sequence in context: A176016 A184833 A281385 * A075464 A247858 A247860

Adjacent sequences:  A279267 A279268 A279269 * A279271 A279272 A279273

KEYWORD

sign

AUTHOR

Michael Somos, Dec 09 2016

STATUS

approved

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Last modified October 23 02:14 EDT 2019. Contains 328335 sequences. (Running on oeis4.)