A113423 Expansion of q^(-1)eta(q^2)*eta(q^8)^2*eta(q^10)/eta(q^4) in powers of q^2.

1, -1, 0, -1, -1, 0, 2, 1, 0, 2, -2, 1, -1, 2, -2, -2, -2, -1, 0, 2, 2, -3, 0, 1, 1, 2, 2, 0, 2, -2, 0, 1, 0, -3, 2, -2, 0, 1, -2, -4, -1, 1, 2, -4, 0, 2, 0, 0, 0, 0, 2, 3, 0, 3, 0, 2, -2, -1, -2, 2, -1, 0, 0, 7, 2, 0, -6, -2, -2, -2, -2, -2, 0, -3, 0, 2, 0, 0, 4, -2, -2, 5, -2, -1, 1, -2, 0, 1, 2, 2, -2, 0, 2, 2, 4, -2, 4, 0, 2, 0, -2, 2, 0, -3, 0

Offset

0,7

Links

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

K. Ono, Ramanujan, taxicabs, birthdates, ZIP codes and twists, Amer. Math. Monthly, 104 (1997), 912-917, MR1490909 (98i:11020).

Formula

Euler transform of period 20 sequence [ -1, 0, -1, -2, -2, 0, -1, -2, -1, -1, -1, -2, -1, 0, -2, -2, -1, 0, -1, -3, ...].

Example

q -q^3 -q^7 -q^9 +2*q^13 +q^15 +2*q^19 -2*q^21 +q^23 +...

Mathematica

a[n_] := SeriesCoefficient[QPochhammer[q^2]* QPochhammer[q^8]^2*
QPochhammer[q^10]/QPochhammer[q^4], {q, 0, n}]; Table[a[n], {n, 0, 100}][[;; ;; 2]] (* G. C. Greubel, Mar 10 2017 *)

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^4+A)^2*eta(x^5+A)/eta(x^2+A), n))}

Crossrefs

Sequence in context: A372626 A305152 A170983 * A131258 A298596 A029366

Adjacent sequences: A113420 A113421 A113422 * A113424 A113425 A113426

Keyword

sign

Author

Michael Somos, Oct 31 2005

Status

approved