unexpected EIS hit

[wouter meeussen]

define f[a[1..N],n] as Sum(d|n, a[1]a[d]+a[2]a[d-1]+..+a[d]a[1] ),N>=n

then f[ {1,2,3,4,..},n]=
{1,5,11,25,36,71,85,145,176,260,287,455,456,649,726
=ID Number: A059358
=Coefficients in expansion of Sum_{n >= 1} x^n/(1-x^n)^4

I don't see the 'why'. Who does?

the moebius transform of A059358 is
A000292 (Tetrahedral (or pyramidal) numbers: C(n+3,3),
        Also the convolution of the natural numbers with themselves )
..and this makes sense (Moebius inversion formula).

But why Sum x^n/(1-x^n)^4 ???
Any combinatorial significance?

in Mathematica:
  f[li:{__Integer},n_Integer]:=Fold[#1+ (Reverse at Take[li,#2]. Take[li,#2])
&,0,Divisors[n]];
  Table[f[Range[48],k],{k,48}]


Wouter Meeussen
wouter.meeussen at pandora.be




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