A143159 Expansion of q^(-13/24) * eta(q^2) * eta(q^3) * eta(q^4)^2 in powers of q.

1, 0, -1, -1, -3, 1, 1, 3, 2, -2, 5, -1, 1, -2, -4, -2, -3, 2, -7, -2, 4, 7, 0, -1, -1, 0, 4, 10, 5, -7, 7, -3, -6, -3, 0, -1, -5, -6, 3, -7, 1, 5, -5, 1, -4, 1, -9, 7, 2, 16, 2, -2, 8, 2, 5, 2, 5, -11, -4, -1, 1, 1, -2, 2, 6, -12, 7, -9, -9, 1, -15, -2, 1, -4

Offset

0,5

Links

Table of n, a(n) for n=0..73.

Formula

Euler transform of period 12 sequence [0, -1, -1, -3, 0, -2, 0, -3, -1, -1, 0, -4, ...].

G.f.: Product_{k>0} (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k))^2.

Example

G.f. = 1 - x^2 - x^3 - 3*x^4 + x^5 + x^6 + 3*x^7 + 2*x^8 - 2*x^9 + ...
G.f. = q^13 - q^61 - q^85 - 3*q^109 + q^133 + q^157 + 3*q^181 + 2*q^205 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x^2] QPochhammer[ x^3] QPochhammer[ x^4]^2, {x, 0, n}]; (* Michael Somos, Sep 07 2015 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^4 + A)^2, n))};

Crossrefs

Sequence in context: A023142 A225335 A229166 * A324079 A184831 A033989

Adjacent sequences: A143156 A143157 A143158 * A143160 A143161 A143162

Keyword

sign

Author

Michael Somos, Jul 27 2008

Status

approved