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A254346 Expansion of f(x, x^5) * f(-x^6) / f(x)^2 in powers of x where f() is a Ramanujan theta function. 3
1, -1, 3, -5, 10, -15, 26, -39, 63, -92, 140, -201, 295, -415, 591, -818, 1140, -1554, 2126, -2861, 3855, -5126, 6816, -8970, 11793, -15372, 20007, -25857, 33356, -42771, 54734, -69683, 88530, -111968, 141312, -177642, 222842, -278557, 347484, -432095, 536230 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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) * eta(q^3) * eta(q^4) * eta(q^12) / eta(q^2)^4 in powers of q.
Euler transform of period 12 sequence [ -1, 3, -2, 2, -1, 2, -1, 2, -2, 3, -1, 0, ...].
a(n) = (-1)^n * A132302(n). 2 * a(n) = A254372(2*n + 1).
EXAMPLE
G.f. = 1 - x + 3*x^2 - 5*x^3 + 10*x^4 - 15*x^5 + 26*x^6 - 39*x^7 + ...
G.f. = q - q^3 + 3*q^5 - 5*q^7 + 10*q^9 - 15*q^11 + 26*q^13 - 39*q^15 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^3] QPochhammer[ x^12] / (QPochhammer[ x^2] QPochhammer[ -x]), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A) / eta(x^2 + A)^4, n))};
CROSSREFS
Sequence in context: A070557 A225751 A264397 * A132302 A308872 A097513
KEYWORD
sign
AUTHOR
Michael Somos, Jan 29 2015
STATUS
approved

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Last modified June 13 15:51 EDT 2024. Contains 373389 sequences. (Running on oeis4.)