The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com
Permutations of length n can be represented by an ordered list of the first n integers. Summing vertically the lists corresponding to the successive powers of a permutation up to its order ord, gives a new list of n integers from ord to n*ord. a(n) gives the number of different such lists. a(n) is related to the Bell numbers and majored by them, as permutations with the same cycle decomposition will have the same order and only a different ordering of powers.