A156215 Expansion of (chi(q^3) / chi(q))^6 + q / (chi(q^3) / chi(q))^6 in powers of q where chi() is a Ramanujan theta function.

1, -5, 27, -41, 146, -243, 510, -887, 1755, -2728, 5052, -7857, 13157, -20253, 32805, -48680, 76568, -112320, 169814, -246263, 365013, -519046, 755632, -1063368, 1516404, -2112551, 2972160, -4089098, 5683166, -7750782, 10633276, -14382932, 19539387

Offset

0,2

Comments

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

Denoted by "(24~e)" in Simon Norton's replicable function list.

Links

Table of n, a(n) for n=0..32.

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of (chi(q) * chi(q^3))^3 - 8 * q / (chi(q) * chi(q^3))^3 in powers of q where chi() is a Ramanujan theta function.

G.f. is a period 1 Fourier series which satisfies f(-1 / (48 t)) = f(t) where q = exp(2 Pi i t).

a(n) = (-1)^n * A058490(n).

Example

G.f. = 1 - 5*x + 27*x^2 - 41*x^3 + 146*x^4 - 243*x^5 + 5120*x^6 + ...
G.f. = 1/q - 5*q + 27*q^3 - 41*q^5 + 146*q^7 - 243*q^9 + 510*q^11 - 887*q^13 + ...

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); A = ((eta(x^2 + A) * eta(x^6 + A))^2 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A)))^3; polcoeff( A - 8 * x / A, n))};

Crossrefs

Cf. A058490.

Sequence in context: A056735 A298441 A056154 * A058490 A299578 A308829

Adjacent sequences: A156212 A156213 A156214 * A156216 A156217 A156218

Keyword

sign

Author

Michael Somos, Feb 06 2009

Status

approved