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A263444
Expansion of psi(q)^2 * chi(-q^6)^2 * f(-q^6) in powers of q where psi(), chi(), f() are Ramanujan theta functions.
2
1, 2, 1, 2, 2, 0, 0, -4, -3, -4, -4, 2, -6, 0, 2, 0, 2, -6, 4, -4, 0, 0, -8, 4, 0, 14, 2, 2, 12, 0, 8, -4, -3, 0, -4, 4, -4, 0, 4, 8, 12, -6, 0, -12, -6, 0, -8, 4, -6, 14, 5, 0, 0, 0, 0, -8, -6, -24, -12, 2, 0, 0, 6, 8, 2, -12, 8, -12, -6, 0, -8, 4, -12, 24, 6
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 psi(q)^2 * phi(-q^3) * chi(q^3)^2 in powers of q where psi(), phi(), chi() are Ramanujan theta functions.
Expansion of eta(q^2)^4 * eta(q^6)^3 / (eta(q)^2 * eta(q^12)^2) in powers of q.
Euler transform of period 12 sequence [ 2, -2, 2, -2, 2, -5, 2, -2, 2, -2, 2, -3, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = 15552^(1/2) (t/i)^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A263433.
a(8*n + 5) = a(9*n + 6) = 0.
EXAMPLE
G.f. = 1 + 2*x + x^2 + 2*x^3 + 2*x^4 - 4*x^7 - 3*x^8 - 4*x^9 - 4*x^10 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q^(1/2)]^2 QPochhammer[ q^6, q^12]^2 QPochhammer[ q^6] / (4 q^(1/4)), {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^6 + A)^3 / (eta(x + A)^2 * eta(x^12 + A)^2), n))};
CROSSREFS
Cf. A263433.
Sequence in context: A230322 A174950 A159906 * A276321 A152196 A024375
KEYWORD
sign
AUTHOR
Michael Somos, Oct 18 2015
STATUS
approved