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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. 7
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
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
Sequence in context: A279497 A359305 A138330 * A354747 A254444 A102005
KEYWORD
nonn
AUTHOR
Michael Somos, Mar 11 2007
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)