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A255317
Expansion of psi(-x^3)^2 / chi(-x) in powers of x where psi(), chi() are Ramanujan theta functions.
7
1, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1
OFFSET
0,8
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(x^6) * f(x, x^2) in powers of x where psi(), f() are Ramanujan theta functions.
Expansion of q^(-19/24) * eta(q^2) * eta(q^3)^2 * eta(q^12)^2 / (eta(q) * eta(q^6)^2) in powers of q.
Euler transform of period 12 sequence [ 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, -2, ...].
EXAMPLE
G.f. = 1 + x + x^2 + x^5 + x^6 + 2*x^7 + x^8 + x^11 + x^12 + x^13 + ...
G.f. = q^19 + q^43 + q^67 + q^139 + q^163 + 2*q^187 + q^211 + q^283 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x] EllipticTheta[ 2, Pi/4, x^(3/2)]^2 / (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^2 + A) * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A) * eta(x^6 + A)^2), n))};
CROSSREFS
Sequence in context: A118229 A172250 A309047 * A309168 A179229 A117201
KEYWORD
nonn
AUTHOR
Michael Somos, Feb 21 2015
STATUS
approved