login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A257469
Expansion of f(-x) * psi(x^6) in powers of x where psi(), f() are Ramanujan theta functions.
2
1, -1, -1, 0, 0, 1, 1, 0, -1, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, -1, -1, -1, 1, 1, 0, 1, 1, 0, 1, 0, -1, 0, 1, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0, 1, 1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 1, -1, 0, 1, 0, 1, 0, 1, 0, 1, -1, -1, -1, 0, 0, 0, -2, -1, 0
OFFSET
0,58
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^(-19/24) * eta(q) * eta(q^12)^2 / eta(q^6) in powers of q.
Euler transform of period 12 sequence [ -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -2, ...].
-2 * a(n) = A246962(3*n + 2).
EXAMPLE
G.f. = 1 - x - x^2 + x^5 + x^6 - x^8 + x^11 - x^12 + x^13 - x^15 - x^19 + ...
G.f. = q^19 - q^43 - q^67 + q^139 + q^163 - q^211 + q^283 - q^307 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x] EllipticTheta[ 2, 0, x^3] / (2 x^(3/4)), {x, 0 , n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^12 + A)^2 / eta(x^6 + A), n))};
CROSSREFS
Cf. A246962.
Sequence in context: A213185 A285716 A101606 * A275947 A337976 A378150
KEYWORD
sign
AUTHOR
Michael Somos, Apr 25 2015
STATUS
approved