A258770 Expansion of f(-x^2)^4 * psi(-x^3) in powers of x where psi(), f() are Ramanujan theta functions.

1, 0, -4, -1, 2, 4, 8, -2, -5, -9, -4, 9, -10, 2, 8, 2, 9, -3, 1, -5, 10, 10, -14, -22, -2, 7, -9, 10, -4, -10, -17, 16, 18, 18, 31, -10, 10, -20, 9, 6, -31, -14, 0, -9, -28, -23, -7, 36, -8, 25, 24, -28, 18, 41, 0, 6, -13, 2, 9, 5, 38, -43, -18, -35, 6, -1

Offset

0,3

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^(-17/24) * eta(q^2)^4 * eta(q^3) * eta(q^12) / eta(q^6) in powers of q.

Euler transform of period 12 sequence [ 0, -4, -1, -4, 0, -4, 0, -4, -1, -4, 0, -5, ...].

G.f.: Product_{k>0} (1 - x^(2*k))^4 * (1 - x^(3*k)) * (1 + x^(6*k)).

16 * a(n) = A258771(3*n + 2).

Example

G.f. = 1 - 4*x^2 - x^3 + 2*x^4 + 4*x^5 + 8*x^6 - 2*x^7 - 5*x^8 - 9*x^9 + ...
G.f. = q^17 - 4*q^65 - q^89 + 2*q^113 + 4*q^137 + 8*q^161 - 2*q^185 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^4 QPochhammer[ x^3] / QPochhammer[ x^6, x^12], {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n), polcoeff( eta(x^2 + A)^4 * eta(x^3 + A) * eta(x^12 + A) / eta(x^6 + A), n))};

Crossrefs

Cf. A258771.

Sequence in context: A324466 A152523 A082903 * A225815 A154589 A354104

Adjacent sequences: A258767 A258768 A258769 * A258771 A258772 A258773

Keyword

sign

Author

Michael Somos, Jun 09 2015

Status

approved