[seqfan] Re: A112194, McKay-Thompson series
Allan Wechsler
acwacw at gmail.com
Tue Jul 21 22:23:08 CEST 2015
Haskell code for Keith's sequence:
a112194 n = a n 0 n
a maxEntry numTimesUsed n =
if maxEntry > n
then (a n 0 n)
else if numTimesUsed >= 2 || (mod maxEntry 3) == 0
then (a (maxEntry - 1) 0 n)
else if n == 0
then 1
else if maxEntry < 1
then 0
else ((a maxEntry (numTimesUsed + 1) (n - maxEntry)) + (a
(maxEntry - 1) 0 n))
I confirm that for n in [0..55], it produces results equal to those
reported for a112194.
On Tue, Jul 21, 2015 at 3:16 PM, William Keith <william.keith at gmail.com>
wrote:
> Sequence fans:
>
> Does anyone have any expertise with this subject? Sequence A112194
> appears to have generating function \prod_{3 \nmid k} (1+q^k+q^{2k}) ,
> i.e., it is the generating function of partitions into parts not divisible
> by 3 which may appear fewer than three times. (The actual series T54c
> appears to be this as a function of q^6 instead of q, multiplied by 1/q.)
> This is probably well known among people who study the Monster group, but I
> am not one of them.
>
> Cordially,
> William Keith
>
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