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 A192553 Sums of powers of permutations of length n. 0
 1, 2, 5, 15, 51, 197, 850, 3897, 19461, 104264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Table of n, a(n) for n=1..10. FORMULA a(n) <= Bell(n) EXAMPLE {2, 1, 3, 6, 4, 5} is a permutation of length 6 and order 6. Its successive powers are {2, 1, 3, 6, 4, 5}, {1, 2, 3, 5, 6, 4}, {2, 1, 3, 4, 5, 6}, {1, 2, 3, 6, 4, 5}, {2, 1, 3, 5, 6, 4}, {1, 2, 3, 4, 5, 6}. Their sum is {9, 9, 18, 30, 30, 30} or {8, 7, 15, 26, 25, 24} if one does not includes the identity. There are 197 different sums for n=6. CROSSREFS Cf. A000110, A051625. Sequence in context: A201168 A001681 A343665 * A053553 A276721 A287583 Adjacent sequences: A192550 A192551 A192552 * A192554 A192555 A192556 KEYWORD nonn AUTHOR Olivier Gérard, Jul 04 2011 STATUS approved

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Last modified April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)