1,2

Sum (number of cycles) over all n! permutations of [1..n] gives A000254.

N. J. A. Sloane, Table of n, a(n) for n = 1..30

a(n) = (-1)^(n+1)*(Stirling1(n+1,2)-2*Stirling1(n+1,3)). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Jul 22 2009]

with(combinat): with(numtheory):

M:=30;

for n from 1 to M do

p:=partition(n); s:=0:

for k from 1 to nops(p) do

# get next partition of n

# convert partition to list of sizes of parts

q:=convert(p[k], multiset);

for i from 1 to n do a(i):=0: od:

for i from 1 to nops(q) do a(q[i][1]):=q[i][2]: od:

# get number of parts

nump := add(a(i), i=1..n);

# get multiplicity

c:=1: for i from 1 to n do c:=c*a(i)!*i^a(i): od:

prop:=nump^2;

s:=s + (n!/c)*prop;

od;

lprint(n, s);

A[n]:=s;

od:

[seq(A[n], n=1..M)];

Cf. A000254, A151882.

Sequence in context: A005393 A162815 A033312 this_sequence A121636 A020032 A009321

Adjacent sequences: A151878 A151879 A151880 this_sequence A151882 A151883 A151884

nonn

N. J. A. Sloane (njas(AT)research.att.com), Jul 22 2009