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 A365229 Sum over all k of 1/k! times the number of permutations of [n] for which the difference between the longest and the shortest cycle length is k. 2
 1, 1, 2, 6, 20, 85, 382, 2219, 13624, 100293, 811914, 7594015, 74507490, 862987151, 10327793088, 139175089681, 1966790900028, 30983071424315, 496696984054286, 8925920862110603, 162253809011669330, 3228438870635420315, 65677024568975412036, 1448358661756969370985 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(0) = 1 by convention. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..275 Wikipedia, Permutation FORMULA a(n) = Sum_{k=0..max(0,n-2)} A364967(n,k)/k!. a(n) mod 2 = A000035(n) for n>=4. MAPLE b:= proc(n, l, m) option remember; `if`(n=0, 1/(m-l)!, add((j-1)! *b(n-j, min(l, j), max(m, j))*binomial(n-1, j-1), j=1..n)) end: a:= n-> b(n\$2, 0): seq(a(n), n=0..23); CROSSREFS Cf. A000035, A000142, A364967. Sequence in context: A177474 A372987 A177480 * A089179 A177483 A004104 Adjacent sequences: A365226 A365227 A365228 * A365230 A365231 A365232 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 27 2023 STATUS approved

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Last modified September 7 22:13 EDT 2024. Contains 375749 sequences. (Running on oeis4.)