Re: Computing the number of partition tuples...

[Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>]

* Andrew Mathas [2012-09-21 03:51]:
> I am using pari (through sage) to compute the number of k-tuples of
> partitions which sum to n. The relevant command to compute the
> number of 2-tuples of partitions of 16 inside pari is
> 
>    ? polcoeff(1/eta(x)^2, 16, x)
>    5822
> 
> which is correct. However, when I try to compute the number of
> 2-tuples of partitions of 17 (which is 8470) then I get
> 
>    ? polcoeff(1/eta(x)^2, 17, x)
>       ***   at top-level: polcoeff(1/eta(x)^2,
>       ***                 ^--------------------
>       *** polcoeff: non existent component in truecoeff.
>       ***   Break loop: type 'break' to go back to GP
> 
> Is this a bug or am I doing something wrong?

(08:12) gp > 1/eta(x)^2
%1 = 1 + 2*x + 5*x^2 + 10*x^3 + 20*x^4 + 36*x^5 + 65*x^6 + 110*x^7 + 185*x^8 + 300*x^9 + 481*x^10 + 752*x^11 + 1165*x^12 + 1770*x^13 + 2665*x^14 + 3956*x^15 + 5822*x^16 + O(x^17)

The series precision is too low, so the 17-th coefficient is unknown. Use

  1/eta(x + O(x^101))

if you want to access its 100-th coefficient (for instance).

Cheers,

    K.B.
-- 
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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