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A256004 Expansion of q^3 * f( -q, -q^8)^4 * f( -q^2, -q^7) / (f( -q) * f( -q^4, -q^5)^2) in powers of q where f() is Ramanujan's general theta function. 1
1, -3, 3, 0, 0, -3, 1, 3, 0, -2, -3, 3, 3, -3, 0, 0, 0, 0, 2, -3, 3, -3, 3, -3, 1, 0, 0, 3, -3, 0, 0, 0, 3, -2, 0, 0, -1, -3, 3, 3, 0, -6, 3, 3, 0, -2, -3, 6, 0, -6, 0, 0, 3, 0, 2, -3, 3, 0, 0, -3, 2, 0, 0, -3, -3, 0, 3, 6, 0, -3, 0, 0, 4, -6, 3, -3, 0, -3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
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
Euler transform of period 9 sequence [ -3, 0, 1, 3, 3, 1, 0, -3, -2, ...].
EXAMPLE
G.f. = q^3 - 3*q^4 + 3*q^5 - 3*q^8 + q^9 + 3*q^10 - 2*q^12 - 3*q^13 + ...
MATHEMATICA
a[ n_] := If[ n < 3, 0, With[{m = n - 3}, SeriesCoefficient[ q^3 Product[ (1 - q^k)^{3, 0, -1, -3, -3, -1, 0, 3, 2}[[Mod[k, 9, 1]]], {k, m}], {q, 0, n}]]];
PROG
(PARI) {a(n) = if( n<3, 0, n-=3; polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[2, 3, 0, -1, -3, -3, -1, 0, 3][k%9 + 1]), n))};
(Magma) Basis( ModularForms( Gamma1(9), 1), 82) [4];
CROSSREFS
Sequence in context: A342697 A360480 A257094 * A269707 A109247 A021307
KEYWORD
sign
AUTHOR
Michael Somos, May 06 2015
STATUS
approved

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Last modified May 26 21:09 EDT 2024. Contains 372844 sequences. (Running on oeis4.)