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A255257
Expansion of psi(x) * phi(-x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
1
1, 1, -4, -3, 4, 0, 1, 4, 0, 4, -3, -4, -4, -8, 8, 1, -4, 0, 0, 4, 0, 5, 4, 8, -4, -4, 4, -8, -3, -4, 4, -4, 0, 0, -8, 4, 1, 0, -8, 0, 4, 8, 8, 8, 0, 1, 0, -8, 8, -4, -4, -8, 12, 4, -12, 1, -4, 0, 0, -4, -8, 4, -8, 0, 0, -8, 1, 12, 8, 8, 0, -8, 8, 0, 8, 4, 0
OFFSET
0,3
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 q^(-1/8) * eta(q^2)^6 / (eta(q) * eta(q4)^2) in powers of q.
Euler transform of period 4 sequence [ 1, -5, 1, -3, ...].
a(n) = A034950(4*n).
EXAMPLE
G.f. = 1 + x - 4*x^2 - 3*x^3 + 4*x^4 + x^6 + 4*x^7 + 4*x^9 - 3*x^10 + ...
G.f. = q + q^9 - 4*q^17 - 3*q^25 + 4*q^33 + q^49 + 4*q^57 + 4*q^73 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^2] ^2 EllipticTheta[ 2, 0, x^(1/2)] / (2 x^(1/8)), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^6 / (eta(x + A) * eta(x^4 + A)^2), n))};
CROSSREFS
Cf. A034950.
Sequence in context: A309046 A007568 A091884 * A306769 A336031 A329982
KEYWORD
sign
AUTHOR
Michael Somos, Feb 19 2015
STATUS
approved