[seqfan] Re: The inverse Euler transformation of A035938

William Keith william.keith at gmail.com
Sun Jan 22 18:49:25 CET 2012

On Sun, Jan 22, 2012 at 5:30 PM, N. J. A. Sloane <njas at research.att.com>wrote:

> Peter, That's a very nice discovery. Please make sure it gets added
> (with or without a proof) to that sequence.
> It reminds me a bit of the analysis of restricted
> partitions in Comtet's Advanced Combinatorics,
> Section 2.6, pages 108-115. Perhaps that will suggest a proof.
>  Best regards
>                         Neil

What does EULERi do?  If, as I guess, it gives the exponents b_i such that
the generating function of the data sequence is \prod 1/(1-q^k)^{b_i}, then
the 1-0 sequence given is recording Gordon's Theorem itself: entries 7k,
7k+2, and 7k-2 are 0, and others are 1, giving the generating function for
partitions into parts not 7k, 7k+2, or 7k-2.

William Keith

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