# Could someone compute a few more terms for A006128 ?

Robert G. Wilson v rgwv at rgwv.com
Tue Nov 8 01:33:26 CET 2005

```Dear Thomas,

The first 100 terms using the Mathematica coding of:
CoefficientList[ Series[ Sum[n*x^n*Product[1/(1 - x^k), {k, n}], {n,100}], {x, 0, 100}], x]
in 0.13 seconds is

{0, 1, 3, 6, 12, 20, 35, 54, 86, 128, 192, 275, 399, 556, 780, 1068, 1463, 1965, 2644, 3498, 4630, 6052, 7899, 10206, 13174, 16851, 21522, 27294, 34545, 43453, 54563, 68135, 84927, 105366, 130462, 160876, 198014, 242812, 297201, 362587, 441546, 536104, 649791, 785437, 947812, 1140945, 1371173, 1644136, 1968379, 2351597, 2805218, 3339869, 3970648, 4712040, 5584141, 6606438, 7805507, 9207637, 10847703, 12760906, 14993151, 17591088, 20614860, 24126393, 28203987, 32929312, 38404426, 44736332, 52057537, 60508103, 70259278, 81493581, 94432246, 109311863, 126417307, 146054892, 168590041, 194417783, 224006431, 257863391, 296587112, 340828172, 391348925, 448980978, 514694110, 589547701, 674772306, 771715076, 881933249, 1007135164, 1149288434, 1310553403, 1493410529, 1700586677, 1935201437, 2200688624, 2500965274, 2840344772, 3223735387, 3656545760, 4144913179}

You may have more is so desired.

Sincerely, Bob.

Emeric Deutsch wrote:

>
> Take only the first 60 terms of the given g.f.
>
> g:=sum(n*x^n*product(1/(1-x^k),k=1..n),n=1..60):
>
> We are neglecting terms starting from x^61.
>
> Maple gives at once the following coefficients of the series of g:
>
> [0, 1, 3, 6, 12, 20, 35, 54, 86, 128, 192, 275, 399, 556, 780, 1068,
> 1463, 1965, 2644, 3498, 4630, 6052, 7899, 10206, 13174, 16851, 21522,
> 27294, 34545, 43453, 54563, 68135, 84927, 105366, 130462, 160876,
> 198014, 242812, 297201, 362587, 441546, 536104, 649791, 785437, 947812,
> 1140945, 1371173, 1644136, 1968379, 2351597, 2805218, 3339869, 3970648,
> 4712040, 5584141, 6606438, 7805507, 9207637]
>
> E. Deutsch
>
> On Tue, 8 Nov 2005, Thomas Baruchel wrote:
>
>> Hi,
>>
>> working on the complexity of some function in a library I am currently
>> writing, I would like to have A006128 up to n=48 (or more ;-)
>> I have written a piece of code, but it quickly becomes very slow.
>> Could someone post on seqfan (and add to the database) a few more terms ?
>>
>> Regards,
>>
>> --
>> Thomas Baruchel