OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of psi(x)^4 / phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions.
Expansion of q^(-1/2) * eta(q^2)^10 * eta(q^8)^2 / (eta(q)^4 * eta(q^4)^5) in powers of q.
Euler transform of period 8 sequence [4, -6, 4, -1, 4, -6, 4, -3, ...].
EXAMPLE
G.f. = 1 + 4*x + 4*x^2 + 5*x^4 + 12*x^5 + 4*x^6 + 8*x^8 + 12*x^9 + ...
G.f. = q + 4*q^3 + 4*q^5 + 5*q^9 + 12*q^11 + 4*q^13 + 8*q^17 + 12*q^19 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x]^2 EllipticTheta[ 2, 0, x^2] / (2 x^(1/2)), {x, 0, n}];
a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, x^(1/2)]^4 / (16 x^(1/2) EllipticTheta[ 3, 0, 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)^10 * eta(x^8 + A)^2 / (eta(x + A)^4 * eta(x^4 + A)^5), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 03 2014
STATUS
approved