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A263528
Expansion of (psi(x) * psi(x^3) / f(-x^3)^2)^2 in powers of x where psi(), f() are Ramanujan theta functions.
3
1, 2, 1, 8, 14, 6, 38, 60, 23, 140, 208, 76, 439, 626, 221, 1232, 1704, 584, 3182, 4300, 1443, 7700, 10212, 3368, 17673, 23076, 7497, 38808, 50008, 16046, 82070, 104560, 33190, 167996, 211920, 66628, 334202, 417902, 130288, 648224, 804254, 248858, 1229148
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^(-1/2) * (eta(q^2)^2 * eta(q^6)^2 / (eta(q) * eta(q^3)^3))^2 in powers of q.
Euler transform of period 6 sequence [ 2, -2, 8, -2, 2, 0, ...].
-2 * a(n) = A262930(2*n + 1).
EXAMPLE
G.f. = 1 + 2*x + x^2 + 8*x^3 + 14*x^4 + 6*x^5 + 38*x^6 + 60*x^7 + 23*x^8 + ...
G.f. = q + 2*q^3 + q^5 + 8*q^7 + 14*q^9 + 6*q^11 + 38*q^13 + 60*q^15 + 23*x^17 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (EllipticTheta[ 2, 0, x^(1/2)] EllipticTheta[ 2, 0, x^(3/2)] / (4 QPochhammer[ x^3]^2))^2 / x, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 * eta(x^6 + A)^2 / (eta(x + A) * eta(x^3 + A)^3))^2, n))};
CROSSREFS
Cf. A262930.
Sequence in context: A151501 A102735 A088960 * A121360 A199928 A047688
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 19 2015
STATUS
approved