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A263923
Expansion of psi(-x^3)^2 * f(-x^2)^3 / f(-x)^2 in powers of x where psi(), f() are Ramanujan theta functions.
1
1, 2, 2, 2, 1, 2, 3, 4, 5, 2, 3, 4, 4, 4, 3, 4, 4, 4, 5, 4, 3, 8, 7, 6, 4, 4, 6, 4, 9, 6, 4, 4, 4, 8, 5, 6, 9, 4, 7, 6, 7, 10, 6, 10, 7, 4, 9, 10, 5, 6, 6, 10, 6, 6, 9, 4, 9, 8, 10, 6, 6, 12, 8, 12, 8, 6, 10, 8, 13, 6, 6, 8, 12, 12, 6, 8, 10, 12, 11, 10, 7, 8
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^(-11/12) * eta(q^2)^3 * eta(q^3)^2 * eta(q^12)^2 / (eta(q)^2 * eta(q^6)^2) in powers of q.
Euler transform of period 12 sequence [ 2, -1, 0, -1, 2, -1, 2, -1, 0, -1, 2, -3, ...].
-2 * a(n) = A263527(4*n + 3).
EXAMPLE
G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + ...
G.f. = q^11 + 2*q^23 + 2*q^35 + 2*q^47 + q^59 + 2*q^71 + 3*q^83 + 4*q^95 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/2) x^(-3/4) EllipticTheta[ 2, Pi/4, x^(3/2)]^2 QPochhammer[ x^2]^3 / QPochhammer[ x]^2, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A)^2 * eta(x^6 + A)^2), n))};
CROSSREFS
Cf. A263527.
Sequence in context: A179647 A029330 A132225 * A331248 A361913 A253196
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 29 2015
STATUS
approved