OFFSET
0,2
FORMULA
Euler transform of period 6 sequence [-4, -1, -2, -1, -4, -3, ...].
G.f.: Product_{k>=1} (1 - x^k)^4 * (1 - x^(6*k))^4 / ((1 - x^(2*k))^3 * (1 - x^(3*k))^2).
A329955(3*n + 2) = -2 * a(n).
EXAMPLE
G.f. = 1 - 4*x + 5*x^2 - 2*x^3 + 2*x^4 - 6*x^5 + 8*x^6 - 4*x^7 + ...
G.f. = q^2 - 4*q^5 + 5*q^8 - 2*q^11 + 2*q^14 - 6*q^17 + 8*q^20 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x]^4 QPochhammer[ x^6]^5 / (QPochhammer[ x^2]^3 QPochhammer[ x^3]^2), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^6 + A)^4 / (eta(x^2 + A)^3 * eta(x^3 + A)^2), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Nov 29 2019
STATUS
approved