[seqfan] Re: Problem with consistency of A086581 - resolution

[David Scambler]

After email exchange with Maximilian Hasler it is agreed that there are 3 similar but legitimate sequences,
each having different initial terms.

A025242<http://oeis.org/A025242> Generalized Catalan numbers.
A082582<http://oeis.org/A082582> Expansion of (1+x^2-sqrt(1-4x+2x^2+x^4))/(2x) in powers of x.
A086581<http://oeis.org/A086581> Number of Dyck paths of semilength n with no UUDD.

A082582<http://oeis.org/A082582> actually counts "Number of Dyck paths of semilength n with no UUDD" and needs a comment to that effect.
A086581<http://oeis.org/A086581> needs to be renamed to "Number of Dyck paths of semilength n with no DDUU", and the example modified accordingly.

All three need cross references updated.

dave