It has plenty to do with Welsh - the numbers 11 to 20 follow the same pattern as Welsh: i.e 1 & 10, 2 & 10, 3 & 10, 4 & 10, 15,
1 & 15, 2 & 15, 3 & 15, 4 & 15, 20.

See www.answers.com/topic/yan-tan-tethera for versions from various parts of England (Derbyshire, Lancashire, Yorksahire, Westmorland, Cumberland) as well as Welsh, Cornish and Breton equivalents