A143251 Expansion of f(-x, -x^7) * f(-x^2, -x^6) in powers of x where f(,) is Ramanujan's two-variable theta function.

1, -1, -1, 1, 0, 0, -1, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, -1, 2, 0, -1, 0, 0, -2, -1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, -1, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, -1, 0, -1, 0, 1, -1, -1, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, 1, 0, 0, 2, -1, 0, 1, 1, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, 2, 1, 0, -1, 2, 0, 0, 0, 0, 1, 0, 0, -1, -1, -1, 0, 0, 0

Offset

0,23

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

Euler transform of period 8 sequence [ -1, -1, 0, 0, 0, -1, -1, -2, ...].

G.f.: Product_{k>0} (1 - x^(8*k))^2 * (1 - x^(8*k - 1)) * (1 - x^(8*k - 2)) * (1 - x^(8*k - 6)) * (1 - x^(8*k - 7)).

Example

q^13 - q^29 - q^45 + q^61 - q^109 + q^157 + q^173 - q^269 - q^317 + ...

Mathematica

f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A143251[n_] := SeriesCoefficient[f[-x, -x^7]*f[-x^2, -x^6], {x, 0, n}]; Table[A143251[n], {n, 0, 50}] (* G. C. Greubel, Jun 18 2017 *)

Prog

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^([2, 1, 1, 0, 0, 0, 1, 1][k%8 + 1]), 1 + x * O(x^n)), n))}

Crossrefs

Sequence in context: A106594 A357070 A341026 * A115235 A355619 A355607

Adjacent sequences: A143248 A143249 A143250 * A143252 A143253 A143254

Keyword

sign

Author

Michael Somos, Aug 01 2008

Status

approved