[seqfan] A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes

[Vladeta Jovovic]

SeqFans,

There is  Eric Weisstein's recent seq. A158007:  number of simple connected noneulerian graphs on n nodes.
Clearly  A158007(n) = A001349(n) - A003049(n).

Interestingly, it appears that Euler transform of  A158007(n) gives A007126(n+1).

Can someone clarify that connection?

Regards,
Vladeta Jovovic