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A128591 Expansion of  f(x, x^5) * f(x, x^3) in powers of x where f(, ) is Ramanujan's general theta function. 6
1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 0, 0, 1, 2, 2, 1, 1, 1, 1, 2, 3, 1, 1, 0, 2, 1, 1, 2, 0, 2, 0, 2, 1, 0, 4, 2, 0, 1, 1, 2, 1, 2, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 2, 2, 2, 0, 1, 1, 3, 1, 1, 0, 1, 4, 1, 2, 1, 0, 4, 0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 1, 1, 1, 2, 3 (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

Table of n, a(n) for n=0..86.

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of chi(x) * psi(x) * psi(-x^3) in powers of x where psi(), chi() are Ramanujan theta functions. - Michael Somos, Nov 15 2015

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

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

a(n) = A128582(4*n + 1).

2 * a(n) = A257920(3*n + 1). - a(n) = A260118(4*n + 1). 2 * a(n) = A257921(6*n + 2). -2 * a(n) = A128580(12*n + 5) = A190615(12*n + 5). - Michael Somos, Nov 15 2015

EXAMPLE

G.f. = 1 + 2*x + x^2 + x^3 + x^4 + x^5 + 2*x^6 + x^7 + 2*x^8 + x^9 + x^10 + 3*x^11 + ...

G.f. = q^11 + 2*q^35 + q^59 + q^83 + q^107 + q^131 + 2*q^155 + q^179 + 2*q^203 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 2^(-3/2) x^(-1/2) QPochhammer[ -x, x^2] EllipticTheta[ 2, 0, x^(1/2)] EllipticTheta[ 2, Pi/4, x^(3/2)], {x, 0, n}]; (* Michael Somos, Nov 15 2015 *)

PROG

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

CROSSREFS

Cf. A128580, A128582, A190615, A257920, A257921,A260118.

Sequence in context: A115721 A279497 A138330 * A254444 A102005 A051700

Adjacent sequences:  A128588 A128589 A128590 * A128592 A128593 A128594

KEYWORD

nonn

AUTHOR

Michael Somos, Mar 11 2007

STATUS

approved

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Last modified September 25 21:33 EDT 2017. Contains 292500 sequences.