A255319 Expansion of psi(x^3) * f(x, x^5) in powers of x where psi(), f() are Ramanujan theta functions.

1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 3, 1

Offset

0,9

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 chi(x) * f(-x^6) * f(-x^12) in powers of x where chi(), f() are Ramanujan theta functions.

Expansion of q^(-17/24) * eta(q^2)^2 * eta(q^6) * eta(q^12) / (eta(q) * eta(q^4)) in powers of q.

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

Example

G.f. = 1 + x + x^3 + x^4 + x^5 + 2*x^8 + x^9 + x^10 + x^11 + x^14 + x^16 + ...
G.f. = q^17 + q^41 + q^89 + q^113 + q^137 + 2*q^209 + q^233 + q^257 + q^281 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x^6] QPochhammer[ x^12]  QPochhammer[ -x, x^2], {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^6 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^4 + A)), n))};

Crossrefs

Sequence in context: A262097 A085975 A277778 * A214088 A005091 A353455

Adjacent sequences: A255316 A255317 A255318 * A255320 A255321 A255322

Keyword

nonn

Author

Michael Somos, Feb 21 2015

Status

approved