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A263398
Expansion of phi(-x^2)^6 * psi(x^6) / f(x)^2 in powers of x where phi(), psi(), f() are Ramanujan theta functions.
2
1, -2, -7, 14, 20, -36, -34, 40, 50, -30, -71, 76, 82, -144, -98, 112, 131, -70, -140, 170, 168, -288, -228, 232, 246, -120, -290, 258, 310, -468, -280, 344, 337, -190, -350, 394, 412, -648, -510, 496, 462, -252, -583, 558, 602, -864, -532, 584, 664, -350
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 q^(-2/3) * eta(q)^2 * eta(q^2)^6 * eta(q^12)^2 / (eta(q^4)^4 * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [-2, -8, -2, -4, -2, -7, -2, -4, -2, -8, -2, -5, ...].
8 * a(n) = A245643(3*n + 2).
EXAMPLE
G.f. = 1 - 2*x - 7*x^2 + 14*x^3 + 20*x^4 - 36*x^5 - 34*x^6 + 40*x^7 + ...
G.f. = q^2 - 2*q^5 - 7*q^8 + 14*q^11 + 20*q^14 - 36*q^17 - 34*q^20 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^2]^6 EllipticTheta[ 2, 0, x^3] / (2 x^(3/4) QPochhammer[ -x]^2), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^2 + A)^6 * eta(x^12 + A)^2 / (eta(x^4 + A)^4 * eta(x^6 + A)), n))};
(PARI) q='q+O('q^99); Vec(eta(q)^2*eta(q^2)^6*eta(q^12)^2/(eta(q^4)^4*eta(q^6))) \\ Altug Alkan, Jul 31 2018
CROSSREFS
Cf. A245643.
Sequence in context: A285682 A018363 A187142 * A161702 A114346 A369972
KEYWORD
sign
AUTHOR
Michael Somos, Oct 16 2015
STATUS
approved