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A247223 Expansion of f(-x^5, -x^7) in powers of x where f() is a Ramanujan theta function. 5
1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Euler transform of period 12 sequence [ 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, ...]. - Michael Somos, Jan 10 2015

G.f.: Product_{k>0} (1 - x^(12*k)) * (1 - x^(12*k - 5)) * (1 - x^(12*k - 7)).

EXAMPLE

G.f. = 1 - x^5 - x^7 + x^22 + x^26 - x^51 - x^57 + x^92 + x^100 - x^145 + ...

G.f. = q - q^121 - q^169 + q^529 + q^625 - q^1225 - q^1369 + q^2209 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[q^5, q^12]*QPochhammer[q^7, q^12] *QPochhammer[q^12, q^12], {q, 0, n}]; (* G. C. Greubel, dec 08 2017 *)

PROG

(PARI) {a(n) = my(m = 24*n + 1); if( issquare(m, &m) && (m%12==1 || m%12==11), (-1)^((m+6) \ 12))};

CROSSREFS

Sequence in context: A288926 A027356 A181663 * A186741 A173864 A353348

Adjacent sequences: A247220 A247221 A247222 * A247224 A247225 A247226

KEYWORD

sign

AUTHOR

Michael Somos, Jan 10 2015

STATUS

approved

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Last modified November 29 01:35 EST 2022. Contains 358421 sequences. (Running on oeis4.)