OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q * (psi(q^3)^3 / psi(q)) / (phi(q) * phi(q^3)) in powers of q where phi(), psi() are Ramanujan theta functions.
Expansion of eta(q)^3 * eta(x^4)^2 * eta(x^6) * eta(x^12)^2 / (eta(x^2)^7 * eta(x^3)) in powers of q.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 * (1 - 3*v) - v * (1 - 4*v) * (1 - 3*u)^2.
EXAMPLE
G.f. = q - 3*q^2 + 7*q^3 - 15*q^4 + 30*q^5 - 57*q^6 + 104*q^7 - 183*q^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/4) EllipticTheta[ 2, 0, q^(3/2)]^3 / (EllipticTheta[ 2, 0, q^(1/2)] EllipticTheta[ 3, 0, q] EllipticTheta[ 3, 0, q^3]), {q, 0, n}]
PROG
(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^4 + A)^2 * eta(x^6 + A) * eta(x^12 + A)^2 / (eta(x^2 + A)^7 * eta(x^3 + A)), n))}
CROSSREFS
KEYWORD
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AUTHOR
Michael Somos, Oct 26 2013
STATUS
approved