1,3

May also be called the "weight" of the symmetric group S_n.

W. Feit, R. Lyndon and L. L. Scott, A remark on permutations, Journal of Combinatorial Theory (A) 18 234-235 (1975)

N. Hann, Average Weight of a Random Permutation, preprint, 2002.

R. Mantaci and F. Rakotondrajao, A permutation representation that knows what "Eulerian" means, Discrete Mathematics and Theoretical Computer Science, 4 101-108, (2001)

T. D. Noe, Table of n, a(n) for n=1..100

H. N. Hann, Symmetric Canonical Form

R. Mantaci and F. Rakotondrajao, A permutation representation that knows what "Eulerian" means, Discrete Mathematics and Theoretical Computer Science, 4 101-108, (2001)

a(n)=n!*(0/1+1/2+...+(n-1)/n) = n!*(n - H_n), where H_n = Sum_{k=1..n} 1/k; a(1) = 0, a(2) = 1, a(n) = n*a(n-1) + (n-1)*(n-1)!.

a(n) = n*n! - abs(stirling1(n+1, 2)) (cf. A000254). E.g.f.: (x+(1-x)*ln(1-x))/(1-x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 01 2003

a(n) = T(n, n-1) for the triangle read by rows: [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] where DELTA is the operator defined in A084938 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Nov 30 2003

a(3)=7 since the permutations are 1, (12), (13), (23), (12)(13) and (12)(13). There are 7 transpositions.

ZL :=[S, {S = Set(Cycle(Z), 3 <= card)}, labelled]: seq(combstruct[count](ZL, size=n), n=2..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008

Cf. A000254, A001563, A067369, A067370, A084938.

Sequence in context: A086092 A081894 A128597 this_sequence A072948 A000823 A036944

Adjacent sequences: A067315 A067316 A067317 this_sequence A067319 A067320 A067321

easy,nice,nonn

H. Nick Hann (nickhann(AT)aol.com), Jan 15 2002