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A246816
Expansion of phi(q) * phi(-q^2) * phi(-q^4) in powers of q where phi() is a Ramanujan theta function.
2
1, 2, -2, -4, 0, -4, 0, 8, -2, 6, 8, -4, 0, -12, 0, 8, -4, 8, -10, -12, 0, -8, 0, 8, 8, 14, 8, -16, 0, -4, 0, 16, 6, 16, -16, -8, 0, -20, 0, 8, -8, 8, 16, -20, 0, -20, 0, 16, -8, 18, -10, -8, 0, -12, 0, 24, 0, 16, 24, -12, 0, -20, 0, 24, 12, 8, -16, -28, 0
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 eta(q^2)^7 / (eta(q)^2 * eta(q^4) * eta(q^8)) in powers of q.
Euler transform of period 8 sequence [ 2, -5, 2, -4, 2, -5, 2, -3, ...].
a(n) = (-1)^floor(n/2) * A127786(n). a(2*n) = A246814(n). a(2*n + 1) = 2 * A246815(n).
EXAMPLE
G.f. = 1 + 2*q - 2*q^2 - 4*q^3 - 4*q^5 + 8*q^7 - 2*q^8 + 6*q^9 + 8*q^10 + ...
MATHEMATICA
a[n_]:= SeriesCoefficient[EllipticTheta[3, 0, q]* EllipticTheta[3, 0, -q^2]*EllipticTheta[3, 0, -q^4], {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Nov 30 2017 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 / (eta(x + A)^2 * eta(x^4 + A) * eta(x^8 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 03 2014
STATUS
approved