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A257628 Expansion of 1 - f(-x) in powers of x where f() is a Ramanujan  theta function. 1
0, 1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

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..10000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

G.f.: x + x^2 * (1 - x) + x^3 * (1 - x) * (1 - x^2) + ....

G.f.: Sum_{k>0} -(-1)^k * (x^((3*k^2 - k)/2) + x^((3*k^2 + k)/2)).

G.f.: Sum_{k>0} -(-1)^k * x^((k^2 + k) / 2) / ((1 - x) * (1 - x^2) * ... * (1 - x^k)).

a(n) = - A010815(n) unless n=0. a(0) = 0.

EXAMPLE

G.f. = x + x^2 - x^5 - x^7 + x^12 + x^15 - x^22 - x^26 + x^35 + x^40 + ...

G.f. = q^25 + q^49 - q^121 - q^169 + q^289 + q^361 - q^529 - q^625 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 1 - QPochhammer[ x], {x, 0, n}];

a[ n_] := With[ {m = Sqrt[24 n + 1]}, If[ n > 0 && IntegerQ[m], - KroneckerSymbol[ 12, m], 0]];

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( 1 - eta(x + x * O(x^n)), n))};

(PARI) {a(n) = my(m); if( n>0 && issquare( 24*n + 1, &m), - kronecker( 12, m))};

CROSSREFS

Cf. A010815.

Sequence in context: A288752 A189706 A188321 * A203568 A327974 A286049

Adjacent sequences:  A257625 A257626 A257627 * A257629 A257630 A257631

KEYWORD

sign

AUTHOR

Michael Somos, Jul 12 2015

STATUS

approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)