[seqfan] A002831 incompatible with A002830

Sean A. Irvine sairvin at xtra.co.nz
Tue Sep 9 02:06:35 CEST 2014


The terms of A002831 do not match the description:

A002831:  1, 4, 11, 60, 362, 2987
Computed: 1, 4, 11, 60, 318, 2806, 23445, 314518

If F(x) is the generating function for A002831, then we have

G(x) = exp(sum(F(x^k)/k, k=1..infinity))

is the generating function for A002830.  That is, this transform
permits going from a count of connected graphs to the corresponding
count of total graphs (i.e. included disconnected cases). [As an
aside the corresponding inverse is by Mobius inversion
F(x) = sum(mu(k) * log(G(x^k)) / k, k=1..infinity).]

Applying the g.f. transformation to the "Computed" values yields the
current values for A002830 giving me confidence that the computed
values are correct.

I don't have access to R. C. Read's dissertation, so I cannot verify
where the existing values for a(5) and a(6) came from.

Should I update the entry for A002831 (which some comment about the
original terms), or is some other action appropriate?

Regards,
Sean A. Irvine



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