A169638 Number of multiset permutations of the n initial elements of A005229 with additional element A005229(0)=1.

1, 1, 1, 4, 20, 60, 420, 3360, 30240, 151200, 1663200, 9979200, 129729600, 1816214400, 27243216000, 217945728000, 3705077376000, 66691392768000, 633568231296000, 12671364625920000, 266098657144320000, 5854170457175040000, 134645920515025920000, 1615751046180311040000

Offset: 0

Author

Roger L. Bagula, Apr 04 2010

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..429

Crossrefs

Cf. A169637.

Programs

Maple

N:= 100: # to get a(0) to a(N)
A005229:= proc(n) option remember;
procname(procname(n-2))+procname(n-procname(n-2))
end proc:
A005229(1):= 1: A005229(2):= 1:
V:= Vector(N):
A[0]:= 1: V[1]:= 1:
for n from 1 to N do
  r:= A005229(n);
  V[r]:= V[r]+1;
  A[n]:= A[n-1]*(n+1)/V[r];
od:
seq(A[i],i=0..N); # Robert Israel, Dec 23 2014

Mathematica

Mallows[n_Integer?Positive] := Mallows[n] = Mallows[Mallows[n - 2]] + Mallows[ n - Mallows[n - 2]];
Mallows[0] = Mallows[1] = Mallows[2] = 1;
a[m_] := Length[Permutations[Table[Mallows[i], {i, 0, m}]]];
Table[a[m], {m, 0, 10}]
(* A much better way to compute the terms is to use the multinomials of the multiplicities of the terms of A005229! - Joerg Arndt, Dec 23 2014 *)

Formula

a(n) = number of permutations of the list b[0..n] where b(0)=0 and b(n) = A005229(n) for n>=1.

Extensions

Edited and new name, Joerg Arndt, Dec 23 2014

a(11) to a(23) from Robert Israel, Dec 23 2014