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A112280 Coefficients, read modulo 9, of the cube of q-series (q;q)_oo. 2
1, 6, 0, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The cube-root of g.f. A(x) is an integer series (A112281).

LINKS

Table of n, a(n) for n=0..104.

FORMULA

G.f.: A(x) = Sum_{n>=0} A112282(n) * x^(n*(n+1)/2) where A112282(n) = (-1)^n*(2*n+1) (mod 9).

EXAMPLE

A(x) = 1 + 6*x + 5*x^3 + 2*x^6 + 0*x^10 + 7*x^15 + 4*x^21 +... = (1 - 3*x + 5*x^3 - 7*x^6 + 9*x^10 - 11*x^15 +...) (mod 9).

A(x)^(1/3) = 1 + 2*x - 4*x^2 + 15*x^3 - 60*x^4 + 268*x^5 -+...

Notation: q-series (q;q)_oo = Product_{n>=1} (1-q^n) = 1 + Sum_{n>=1} (-1)^n*[q^(n*(3*n-1)/2) + q^(n*(3*n+1)/2)].

PROG

(PARI) {a(n)=polcoeff(sum(k=0, sqrtint(2*n+1), (((-1)^k*(2*k+1))%9)*x^(k*(k+1)/2)+x*O(x^n)), n)}

CROSSREFS

Cf. A112281 (A(x)^(1/3)), A112282 (nonzero terms), A111983 (variant).

Sequence in context: A196623 A265275 A113024 * A204850 A202394 A202954

Adjacent sequences:  A112277 A112278 A112279 * A112281 A112282 A112283

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 01 2005

STATUS

approved

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Last modified September 23 17:50 EDT 2017. Contains 292363 sequences.