OFFSET
0,5
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
KEYWORD
sign
AUTHOR
Michael Somos, Jul 27 2008
STATUS
approved