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A279255 Expansion of chi(x) * chi(-x^3) * chi(-x^8) * chi(-x^24) in powers of x where chi() is a Ramanujan theta function. 1
1, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, -3, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, -1, -5, 0, 0, 0, -2, 0, 0, 0, 5, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,34

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

Euler transform of period 48 sequence [ 1, -1, 0, 0, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, -2, 1, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, 0, 1, -1, 0, -1, 1, -1, 1, 0, 0, -1, 1, 0, ...].

a(4*n + 2) = a(4*n + 3) = a(6*n + 2) = a(6*n + 4) = 0.

a(4*n + 1) = a(12*n) = A029838(n).

EXAMPLE

G.f. = 1 + x + x^5 - x^9 + x^12 + x^17 - x^24 - x^25 - x^29 + 2*x^33 + ...

G.f. = q^-3 + q^-1 + q^7 - q^15 + q^21 + q^31 - q^45 - q^47 - q^55 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^2] QPochhammer[ x^3, x^6] QPochhammer[ x^8, x^16] QPochhammer[ x^24, x^48], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^8 + A) * eta(x^24 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^16 + A) * eta(x^48 + A)), n))};

CROSSREFS

Cf. A029838.

Sequence in context: A248395 A059483 A067618 * A055029 A126812 A008442

Adjacent sequences:  A279252 A279253 A279254 * A279256 A279257 A279258

KEYWORD

sign

AUTHOR

Michael Somos, Dec 08 2016

STATUS

approved

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Last modified June 18 07:24 EDT 2021. Contains 345098 sequences. (Running on oeis4.)