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A244465
Expansion of f(-x^3, -x^5) in powers of x where f() is Ramanujan's two-variable theta function.
4
1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Euler transform of period 8 sequence [ 0, 0, -1, 0, -1, 0, 0, -1, ...].
G.f.: f(-x^3, -x^5) = Sum_{k in Z} (-1)^k * x^(4*k^2 - k).
a(n) = (-1)^n * A214264(n).
EXAMPLE
G.f. = 1 - x^3 - x^5 + x^14 + x^18 - x^33 - x^39 + x^60 + x^68 - x^95 + ...
G.f. = q - q^49 - q^81 + q^225 + q^289 - q^529 - q^625 + q^961 + q^1089 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^3, x^8] QPochhammer[ x^5, x^8] QPochhammer[ x^8], {x, 0, n}];
PROG
(PARI) {a(n) = issquare( 16*n + 1) * (-1)^n};
CROSSREFS
Cf. A214264.
Sequence in context: A123504 A273511 A104015 * A214264 A173858 A217586
KEYWORD
sign
AUTHOR
Michael Somos, Jun 28 2014
STATUS
approved