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A255318 Expansion of psi(x^3) * f(x^2, x^4) in powers of x where psi(), f() are Ramanujan theta functions. 8
1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 2, 1, 1, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

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 f(x^3) * f(-x^6) / chi(-x^2) in powers of x where chi(), f() are Ramanujan theta functions.

Expansion of q^(-11/24) * eta(q^4) * eta(q^6)^4 / (eta(q^2) * eta(q^3) * eta(q^12)) in powers of q.

Euler transform of period 12 sequence [ 0, 1, 1, 0, 0, -2, 0, 0, 1, 1, 0, -2, ...].

EXAMPLE

G.f. = 1 + x^2 + x^3 + x^4 + x^5 + x^7 + x^9 + x^10 + x^11 + 2*x^13 + ...

G.f. = q^11 + q^59 + q^83 + q^107 + q^131 + q^179 + q^227 + q^251 + q^275 + ...

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A060953 A339367 A082858 * A249223 A115953 A225245

Adjacent sequences:  A255315 A255316 A255317 * A255319 A255320 A255321

KEYWORD

nonn

AUTHOR

Michael Somos, Feb 21 2015

STATUS

approved

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)