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A228831
Expansion of psi(x)^2 * phi(-x^2)^4 in powers of x where phi(), psi() are Ramanujan theta functions.
2
1, 2, -7, -14, 18, 32, -21, -14, 16, -30, -14, -14, -15, 66, 48, 82, -28, -160, 66, -32, -95, 36, -30, 128, -14, -94, 64, 18, 98, 98, 105, -92, -112, -96, -206, -64, -28, 226, -126, -46, 320, 32, 27, -142, 208, -30, -60, 64, -206, 322, -16, -28, -48, -224
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 f(x)^4 * f(-x)^2 in powers of x where f() is a Ramanujan theta function.
Expansion of q^(-1/4) * (eta(q^2)^6 / (eta(q) * eta(q^4)^2))^2 in powers of q.
Euler transform of period 4 sequence [2, -10, 2, -6, ...].
G.f.: (Product_{k>0} (1 - x^(2*k))^3 * (1 + x^k) / (1 + x^(2*k))^2)^2.
EXAMPLE
G.f. = 1 + 2*x - 7*x^2 - 14*x^3 + 18*x^4 + 32*x^5 - 21*x^6 - 14*x^7 + 16*x^8 + ...
G.f. = q + 2*q^5 - 7*q^9 - 14*q^13 + 18*q^17 + 32*q^21 - 21*q^25 - 14*q^29 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ -x]^4, {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))^2, n))};
CROSSREFS
Sequence in context: A319250 A018349 A256798 * A285682 A018363 A187142
KEYWORD
sign
AUTHOR
Michael Somos, Sep 04 2013
STATUS
approved