A259790 Expansion of f(-x)^3 * phi(x^2) in powers of x where phi(), f() are Ramanujan theta functions.

1, -3, 2, -1, 0, 10, -7, 0, -12, -6, 9, 10, 18, 0, -14, -11, 0, -22, 20, -6, 0, 23, 0, 4, -14, 0, 0, 0, 3, 26, -30, 0, 2, -28, 0, 10, -13, 0, 20, 26, 0, 0, 18, 0, 34, -19, -30, -60, 0, 0, 2, -6, 0, -2, 34, 21, -14, 42, 0, 0, -12, 0, 0, 4, 0, -22, -23, 0, -12

Offset

0,2

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-3/8) * eta(q)^3 * eta(q^4)^5 / (eta(q^2)^2 * eta(q^8)^2) in powers of q.

Euler transform of period 8 sequence [ -3, -1, -3, -6, -3, -1, -3, -4, ...].

G.f.: Product_{k>0} (1 - x^k)^3 * (1 + x^(2*k))^2 * (1 - x^(4*k)) / (1 + x^(4*k))^2.

Example

G.f. = 1 - 3*x + 2*x^2 - x^3 + 10*x^5 - 7*x^6 - 12*x^8 - 6*x^9 + 9*x^10 + ...
G.f. = q^3 - 3*q^11 + 2*q^19 - q^27 + 10*q^43 - 7*q^51 - 12*q^67 - 6*q^75 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x]^3 EllipticTheta[ 3, 0, x^2], {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^4 + A)^5 / (eta(x^2 + A)^2 * eta(x^8 + A)^2), n))};

Crossrefs

Sequence in context: A004444 A204533 A357079 * A246654 A370506 A184182

Adjacent sequences: A259787 A259788 A259789 * A259791 A259792 A259793

Keyword

sign,changed

Author

Michael Somos, Jul 05 2015

Status

approved